# EXAMINATION. 6 April 2005 (pm) Subject CT5 Contingencies Core Technical. Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE

Save this PDF as:

Size: px
Start display at page:

Download "EXAMINATION. 6 April 2005 (pm) Subject CT5 Contingencies Core Technical. Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE"

## Transcription

2 1 Explain the difference between a profit vector and a profit signature. [2] 2 A 20-year temporary annuity-due of 1 per annum is issued to a life aged 50 exact. (a) Express the expected present value of the annuity in terms of an assurance function. (b) Hence calculate the value using the mortality table AM92 Ultimate with 4% interest. [3] 3 A life insurance company sells an annual premium whole life assurance policy where the sum assured is payable at the end of the year of death. Expenses are incurred at the start of each policy year, and claim expenses are nil. (a) Write down a recursive relationship between the gross premium provisions at successive durations, with provisions calculated on the premium basis. Define all the symbols that you use. (b) Explain in words the meaning of the relationship. [4] 4 A life insurance company issues an annuity to a life aged 60 exact. The purchase price is 200,000. The annuity is payable monthly in advance and is guaranteed to be paid for a period of 10 years and for the whole of life thereafter. Calculate the annual annuity payment. Basis: Mortality Interest AM92 Ultimate 6% per annum [4] CT5 A2005 2

3 5 A three-state transition model is shown in the following diagram: Alive Sick Dead Assume that the transition probabilities are constant at all ages with = 2%, = 4%, = 1% and = 5%. Calculate the present value of a sickness benefit of 2,000 p.a. paid continuously to a life now aged 40 exact and sick, during this period of sickness, discounted at 4% p.a. and payable to a maximum age of 60 exact. [4] 6 Calculate the probability of survival to age 60 exact using ELT15 (Males) for a life aged 45½ exact using two approximate methods. State any assumptions you make. [5] 7 A joint life annuity of 1 per annum is payable continuously to lives currently aged x and y while both lives are alive. The present value of the annuity payments is expressed as a random variable, in terms of the joint future lifetime of x and y. Derive and simplify as far as possible expressions for the expected present value and the variance of the present value of the annuity. [5] 8 A pension scheme provides a pension on ill-health retirement of 1/80 th of Final Pensionable Salary for each year of pensionable service subject to a minimum pension of 20/80 ths of Final Pensionable Salary. Final Pensionable Salary is defined as the average salary earned in the three years before retirement. Normal retirement age is 65 exact. Derive a formula for the present value of the ill-health retirement benefit for a member currently aged 35 exact with exactly 10 years past service and salary for the year before the calculation date of 20,000. [5] 9 Explain how an insurance company uses risk classification to control the profitability of its life insurance business. [5] CT5 A PLEASE TURN OVER

4 10 You are given the following statistics in respect of the population of Urbania: Males Females Age band Exposed to risk Observed Mortality rate Exposed to risk Observed Mortality rate , , , , , , , , Calculate the directly and indirectly standardised mortality rates for the female lives, using the combined population as the standard population. [6] 11 A life insurance company issues a 25-year with profits endowment assurance policy to a male life aged 40 exact. The sum assured of 100,000 plus declared reversionary bonuses are payable on survival to the end of the term or immediately on death, if earlier. Calculate the monthly premium payable in advance throughout the term of the policy if the company assumes that future reversionary bonuses will be declared at a rate of % of the sum assured, compounded and vesting at the end of each policy year. Basis: Interest Mortality Initial commission Initial expenses Renewal commission Renewal expenses 6% per annum AM92 Select 87.5% of the total annual premium 175 paid at policy commencement date 2.5% of each monthly premium from the start of the second policy year 65 at the start of the second and subsequent policy years Claim expense 2.5% of the claim amount [10] CT5 A2005 4

5 12 (i) By considering a term assurance policy as a series of one year deferred term assurance policies, show that: i A A [5] 1 1 = x: n x: n (ii) Calculate the expected present value and variance of the present value of a term assurance of 1 payable immediately on death for a life aged 40 exact, if death occurs within 30 years. Basis: Interest Mortality Expenses: 4% per annum AM92 Select None [6] [Total 11] CT5 A PLEASE TURN OVER

6 13 A life insurance company issues a 4-year unit-linked endowment assurance contract to a male life aged 40 exact under which level premiums of 1,000 per annum are payable in advance. In the first year, 50% of the premium is allocated to units and 102.5% in the second and subsequent years. The units are subject to a bid-offer spread of 5% and an annual management charge of 0.5% of the bid value of the units is deducted at the end of each year. If the policyholder dies during the term of the policy, the death benefit of 4,000 or the bid value of the units after the deduction of the management charge, whichever is higher, is payable at the end of the year of death. On surrender or on survival to the end of the term, the bid value of the units is payable at the end of the year of exit. The company uses the following assumptions in its profit test of this contract: Rate of growth on assets in the unit fund Rate of interest on non-unit fund cashflows Independent rates of mortality Independent rate of withdrawal Initial expenses Renewal expenses Initial commission Renewal commission Risk discount rate 6% per annum 4% per annum AM92 Select 10% per annum in the first policy year; 5% per annum in the second and subsequent policy years. 150 plus 100% of the amount of initial commission 50 per annum on the second and subsequent premium dates 10% of first premium 2.5% of the second and subsequent years premiums 8% per annum (i) (ii) Calculate the profit margin on the assumption that the office does not zeroise future negative cashflows and that decrements are uniformly distributed over the year. [13] Suppose the office does zeroise future negative cashflows. (a) (b) Calculate the expected provisions that must be set up at the end of each year, per policy in force at the start of each year. Calculate the profit margin allowing for the cost of setting up these provisions. [4] [Total 17] CT5 A2005 6

7 14 (i) Write down in the form of symbols, and also explain in words, the expressions death strain at risk, expected death strain and actual death strain. [6] (ii) A life insurance company issues the following policies: 15-year term assurances with a sum assured of 150,000 where the death benefit is payable at the end of the year of death 15-year pure endowment assurances with a sum assured of 75,000 5-year single premium temporary immediate annuities with an annual benefit payable in arrear of 25,000 On 1 January 2002, the company sold 5,000 term assurance policies and 2,000 pure endowment policies to male lives aged 45 exact and 1,000 temporary immediate annuity policies to male lives aged 55 exact. For the term assurance and pure endowment policies, premiums are payable annually in advance. During the first two years, there were fifteen actual deaths from the term assurance policies written and five actual deaths from each of the other two types of policy written. (a) Calculate the death strain at risk for each type of policy during (b) During 2004, there were eight actual deaths from the term assurance policies written and one actual death from each of the other two types of policy written. Calculate the total mortality profit or loss to the office in the year Basis: Interest Mortality 4% per annum AM92 Ultimate for term assurances and pure endowments PMA92C20 for annuities [13] [Total 19] END OF PAPER CT5 A2005 7

8 Faculty of Actuaries Institute of Actuaries EXAMINATION April 2005 Subject CT5 Contingencies Core Technical EXAMINERS REPORT Introduction The attached subject report has been written by the Principal Examiner with the aim of helping candidates. The questions and comments are based around Core Reading as the interpretation of the syllabus to which the examiners are working. They have however given credit for any alternative approach or interpretation which they consider to be reasonable. M Flaherty Chairman of the Board of Examiners 15 June 2005 Faculty of Actuaries Institute of Actuaries

9 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report 1 The profit vector is the vector of expected end-year profits for policies which are still in force at the start of each year. The profit signature is the vector of expected end-year profits allowing for survivorship from the start of the contract. 1 A 50:20 2 (a) ä 50:20 d (b) 50: A A v p (1 A ) ( ) ä 50: d 3 (a) ' t t x t x t t 1 ( V OP e )(1 i) q ( S) p ( V ) ' where ' t V gross premium provision at time t OP = office premium et expenses incurred at time t i = interest rate in premium/valuation basis S = sum assured p x t is the probability that a life aged x + t survives one year on the premium/valuation mortality basis x t q is the probability that a life aged x + t dies within one year on the premium/valuation mortality basis Page 2

10 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report (b) Income (opening provision plus interest on excess of premium over expense, and provision) equals outgo (death claims and closing provision for survivors) if assumptions are borne out. 4 The value of a pension of 1 p.a. is (12) (12) ä ä where first term is an annuity certain (12) 10 ä 10 1 v (12) d (12) (12) (12) 10 (12) 10 ä60 ä60 ä v 60:10 10 p60ä70 p ä (12) 70 ä 70 11/ / So value of a pension of 1 p.a. is v = So annuity purchased by 200,000 is / = 16,948 Page 3

11 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report 5 The present value is ii t p 40 exp(.05 t) So value is 20 0 t exp ( ) ds 0 t t ii e p dt where ln(1.04) 20 0 t 5% t 2000 e e dt where ln(1.04) , 653 t(.05 ln(1.04)) e (.05 ln(1.04)) Require to calculate 14½ p 45½ ½ p 45½. 14 p 46 p l l (a) Assume deaths uniformly distributed so t p x. x t constant (1 ½) q45 ½ Then ½ q45½ (1 ½ q ) (1 ½.00266) So 14½ p 45½ ( ) (b) Assume that force of mortality is constant across year of age 45 to 46 ½ p 45½ e ½ 45 ln(1 q ) ln( ) ½ p 45½ e ½ So 14½ p 45½ Page 4

12 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report 7 Define a random variable T xy, the lifetime of the joint life status The expected value at a rate of interest i is a xy E( a ) T xy E 1 v T xy T xy 1 E( v ) 1 A xy The variance is var 1 v Txy 1 T var( xy v ) ( Axy ( Axy ) ) 2 2 Axy i where is at (1 ) 1 8 Past Service or t ½ i35 t v z35 t ½ a t ½ t 0 l35 v s z s M D ia Page 5

13 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report Future Service z ia M35 z ia R45 s D35 s D Insurance works on the basis of pooling independent homogeneous risks The central limit theorem then implies that profit can be defined as a random variable having a normal distribution. Life insurance risks are usually independent Risk classification ensures that the risks are homogeneous Lives are divided by risk factors More factors implies better homogeneity But the collection of more factors is restricted by The cost of obtaining data Problems with accuracy of information The significance of the factors The desires of the marketing department Age band 10 Males Females Male Female Total Total Female Total Exposed Exposed Actual Actual Actual Exposed to risk to risk deaths deaths deaths to risk Observed Mortality rate Observed Mortality rate Expected deaths using total mortality rates Expected deaths using female rates Direct Indirect Page 6

14 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report 11 Let P be the monthly premium. Then: EPV of premiums: (12) [40]:25 12Pa P (12) a a [40]:25 [40]:25 (1 25 p[40] v ) (1.06) EPV of benefits: 100,000 (1.06) { (1 ) (1 ) (1 b) 1/ q[40] b v 1 q[40] b v q[40] b v 25 p[40] b v... (1 ) } 100,000 (1 ) where b = ,000 D (1 b) 1/ 2 1 ' 65 ' A i i [40]:25 D[40] 100, / 2 (1.06) ( ) 100, where ' 1.06 i b EPV of expenses: (12) (12) [40]:25 [40]: P P ( a a ) 65[ a 1] P [40]:25 (12) a a (1 p [40]:1 [40]:1 [40] v ) 1 1 (1.06) EPV of claim expense: = Page 7

15 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report Equation of value gives P = P and P = (i) A n : t A x n x:1 t 0 n t 1 0 v 1 x t:1 t 1 t p x A x t:1 1 0 s s x t x t s A v p ds Assuming a uniform distribution of deaths, then s p x t x t s q x t 1 x t:1 x t 1 1 s x t x t 0 0 A v q ds q v ds q iv s 1 x: n n 1 t iv A v. t p x. q x t t 0 i n 1 t 0 v t 1. t px. qx t i A 1 x: n Page 8

16 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report (ii) 1 i 1 i 2 1 x: n x: n x: n var( A ) var( A ) var( A ) i 2 2 A 1 A 1 2 x: n x: n ( ( ) ) : A A v p A v A A 40 v. 40 :30 30 p 40. A v where v = 1/ x: n var( A ) ( ( ) ) ln(1.04) Expected value = i A 1 [40]: ln(1.04) 13 Annual premium Allocation % (1st yr) Risk discount rate 8.0% Allocation % (2nd yr +) Interest on investments 6.0% Man charge Interest on sterling provisions 4.0% B/O spread Minimum death benefit % % 0.50% 5.0% % prm Total Initial expense % 350 Renewal expense % 75 Page 9

17 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report (i) Multiple decrement table x d q x s q x x ( aq ) d x ( aq ) s x ( ap) t 1 ( ap ) Unit fund (per policy at start of year) yr 1 yr 2 yr 3 yr 4 value of units at start of year alloc B/O interest management charge value of units at year end Page 10

18 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report Cash flows (per policy at start of year) yr 1 yr 2 yr 3 yr 4 unallocated premium B/O spread expenses interest man charge extra death benefit end of year cashflow probability in force discount factor expected p.v. of profit premium signature expected p.v. of premiums profit margin 2.76% (ii) (a) To calculate the expected provisions at the end of each year we have (utilising the end of year cashflow figures and decrement tables in (i) above): V V (1.04) ( ap) V V V (1.04) ( ap) V V Page 11

19 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report These need to be adjusted as the question asks for the values in respect of the beginning of the year. Thus we have: Year (ap) 42 = Year (ap) 41 = Year (ap) 40 = (b) Based on the expected provisions calculated in (a) above, the cash flow for years 2, 3 and 4 will be zeroised whilst year 1 will become: = Hence the table blow can now be completed for the revised profit margin. revised end of year cash flow probability in force discount factor expected p.v. of profit profit margin 2.58% 14 (i) The death strain at risk for a policy for year t + 1 (t = 0, 1, 2 ) is the excess of the sum assured (i.e. the present value at time t + 1 of all benefits payable on death during the year t + 1) over the end of year provision. i.e. DSAR for year t + 1 S t 1V The expected death strain for year t + 1 (t = 0, 1, 2 ) is the amount that the life insurance company expects to pay extra to the end of year provision for the policy. i.e. EDS for year t + 1 q( S t 1V ) The actual death strain for year t + 1 (t = 0, 1, 2 t+1 of the death strain random variable ) is the observed value at i.e. ADS for year t + 1 ( S t 1V ) if the life died in the year t to t + 1 = 0 if the life survived to t + 1 Page 12

20 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report (ii) Annual premium for pure endowment with 75,000 sum assured given by: P PE 75, 000 D60 75, a D : Annual premium for term assurance with 150,000 sum assured given by: 150, 000A P P 2P 2P a TA EA PE 45:15 PE 45:15 150, Provisions at the end of the third year: for pure endowment with 75,000 sum assured given by: D PE 60 PE 3V 75, 000 P a D 48: , for term assurance with 150,000 sum assured given by: TA EA PE 3V 3V 3V 150, 000 A ( ) a :12 48:12 150, , , for temporary immediate annuity paying an annual benefit of 25,000 given by: IA 3V 25, 000a 58:2 25, 000( a 1) 58: , 000( a v p a 1) , (1.04) , Page 13

21 Subject CT5 (Contingencies Core Technical) April 2005 Examiners Report Sums at risk: Pure endowment: DSAR = 0 11, = 11, Term assurance: DSAR = 150, = 149, Immediate annuity: DSAR = (47, ,000) = 72, Mortality profit = EDS ADS For term assurance EDS ADS 4985 q 149, , ,340, , ,193, mortality profit = 146, For pure endowment EDS ADS 1995 q 11, , , , , mortality profit = 29, For immediate annuity EDS ADS 995 q 72, , , , , mortality profit = 39, Hence, total mortality profit = 77, END OF EXAMINERS REPORT Page 14

23 1 Describe what is meant by adverse selection in the context of a life insurance company s underwriting process and give an example. [2] 2 Describe how occupation affects morbidity and mortality. [3] 3 A graph of f 0 (t), the probability density function for the random future lifetime, T 0, is plotted on the vertical axis, with t plotted on the horizontal axis, for data taken from the English Life Table No. 15 (Males). You are given that f 0 (t) = t p 0 t 80 and then falls. t. You observe that the graph rises to a peak at around Explain why the graph falls at around t 80. [3] 4 Calculate the value of 1.75 p 45.5 on the basis of mortality of AM92 Ultimate and assuming that deaths are uniformly distributed between integral ages. [3] 5 A population is subject to a constant force of mortality of Calculate: (a) (b) The probability that a life aged 20 exact will die before age exact. The curtate expectation of a life aged 20 exact. [4] (12) 6 Define ä fully in words and calculate its value using PMA92C20 and 60:50:20 PFA92C20 tables for the two lives respectively at 4% interest. [5] CT5 S2005 2

24 7 A life insurance company prices its long-term sickness policies using the following three-state continuous-time Markov model, in which the forces of transition,, and are assumed to be constant: Healthy Sick Dead The company issues a particular long-term sickness policy with a benefit of 10,000 per annum payable continuously while sick, provided that the life has been sick continuously for at least one year. Benefit payments under this policy cease at age 65 exact. Write down an expression for the expected present value of the sickness benefit for a healthy life aged 20 exact. Define the symbols that you use. [5] 8 A life insurance company issues an annuity contract to a man aged 65 exact and his wife aged 62 exact. Under the contract, an annuity of 20,000 per annum is guaranteed payable for a period of 5 years and thereafter during the lifetime of the man. On the man s death, an annuity of 10,000 per annum is payable to his wife, if she is then alive. This annuity commences on the monthly payment date next following, or coincident with, the date of his death or from the 5 th policy anniversary, if later and is payable for the lifetime of his wife. Annuities are payable monthly in advance. Calculate the single premium required for the contract. Basis: Mortality PMA92C20 for the male and PFA92C20 for the female Interest 4% per annum Expenses none [9] CT5 S PLEASE TURN OVER

25 9 A life insurance company issues an annuity policy to two lives each aged 60 exact in return for a single premium. Under the policy, an annuity of 10,000 per annum is payable annually in advance while at least one of the lives is alive. (i) (ii) Write down an expression for the net future loss random variable at the outset for this policy. [2] Calculate the single premium, using the equivalence principle. Basis: Mortality PMA92C20 for the first life, PFA92C20 for the second life Interest 4% per annum Expenses ignored [3] (iii) Calculate the standard deviation of the net future loss random variable at the outset for this policy, using the basis in part (ii). You are given that a 60:60 = at a rate of interest 8.16% per annum. [4] [Total 9] CT5 S2005 4

27 11 A life insurance company issues a three-year unit-linked endowment assurance contract to a male life aged 62 exact under which level annual premiums of 10,000 are payable in advance throughout the term of the policy or until earlier death. 85% of each year s premium is invested in units at the offer price. There is a bid-offer spread in unit values, with the bid price being 95% of the offer price. There is an annual management charge of 1.25% of the bid value of units. Management charges are deducted at the end of each year, before death or maturity benefits are paid. On the death of the policyholder during the term of the policy, there is a benefit payable at the end of the year of death of 20,000, or the bid value of the units allocated to the policy, if greater. On maturity, 115% of the full bid value of the units is payable. The company holds unit provisions equal to the full bid value of the units. It sets up non-unit provisions to zeroise any negative non-unit fund cashflows, other than those occurring in the first year. The life insurance company uses the following assumptions in carrying out profit tests of this contract: Mortality AM92 Ultimate Expenses Initial 600 Renewal 100 at the start of each of the second and third policy years Unit fund growth rate Non-unit fund interest rate Non-unit fund provision basis Risk discount rate 8% per annum 4% per annum AM92 Ultimate mortality, interest 4% per annum 15% per annum Calculate the profit margin on the contract. [14] CT5 S2005 6

28 12 On 1 January 2000, a life insurance company issued joint life whole life assurance policies to couples. Each couple comprised one male and one female life and both were aged 50 exact on 1 January Under each policy, a sum assured of 200,000 is payable immediately on the death of the second of the lives to die. Premiums under each policy are payable annually in advance while at least one of the lives is alive. (i) Calculate the annual premium payable under each policy. Basis: Mortality Interest PMA92C20 for the male PFA92C20 for the female 4% per annum Expenses Initial 1,000 Renewal 5% of each premium payment [5] (ii) On I January 2004, 5,000 of these policies were still in force. Under 100 of these policies only the female life was alive. Both lives were alive under the other 4,900 policies. The company calculates provisions for the policies on a net premium basis, using PMA92C20 and PFA92C20 mortality for the male and female lives respectively and 4% per annum interest. During the calendar year 2004, there was one claim for death benefit, in respect of a policy where the female life only was alive at the start of the year. In addition, one male life died during the year under a policy where both lives were alive at the start of the year. 4,999 of the policies were in force at the end of the year. Calculate the mortality profit or loss for the group of 5,000 policies for the calendar year [9] [Total 14] CT5 S PLEASE TURN OVER

29 13 Under the rules of a pension scheme, a member may retire due to age at any age from exact age 60 to exact age 65. On age retirement, the scheme provides a pension of 1/60 th of Final Pensionable Salary for each year of scheme service, subject to a maximum of 40/60 ths of Final Pensionable Salary. Only complete years of service are taken into account. Final Pensionable Salary is defined as the average salary over the three-year period before the date of retirement. The pension scheme also provides a lump sum benefit of four times Pensionable Salary on death before retirement. The benefit is payable immediately on death and Pensionable Salary is defined as the annual rate of salary at the date of death. You are given the following data in respect of a member: Date of birth 1 January 1979 Date of joining the scheme 1 January 2000 Annual rate of salary at 1 January ,000 Date of last salary increase 1 April 2004 (i) (ii) Derive commutation functions to value the past service and future service pension liability on age retirement for this member as at 1 January State any assumptions that you make and define all the symbols that you use. [12] Derive commutation functions to value the liability in respect of the lump sum payable on death before retirement for this member as at 1 January State any assumptions that you make and define all the symbols that you use. [6] [Total 18] END OF PAPER CT5 S2005 8

30 Faculty of Actuaries Institute of Actuaries EXAMINATION September 2005 Subject CT5 Contingencies Core Technical EXAMINERS REPORT Faculty of Actuaries Institute of Actuaries

31 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report In general, this examination was done well by students who were well prepared. Several questions gave difficulties particularly Question 7 and 12(ii) the latter one being very challenging. To help students comments are attached to those questions where particular points are of relevance. Absence of comments can be indicate that the particular question was generally done well. 1 Adverse selection is the manner in which lives form part of a group, which acts against a controlled process of selecting the lives with respect to some characteristic that affects mortality or morbidity. An example is where a life insurance company does not distinguish between smokers and non-smokers in proposals for term assurance cover. A greater proportion of smokers are likely to select this company in preference to a company that charges different rates to smokers and non-smokers. This would be adverse to the company s selection process, if the company had assumed that its proportion of smokers was similar to that in the general population. Other examples were credited. 2 Occupation can have several direct effects on mortality and morbidity. Occupation determines a person s environment for 40 or more hours each week. The environment may be rural or urban, the occupation may involve exposure to harmful substances e.g. chemicals, or to potentially dangerous situations e.g. working at heights. Much of this is moderated by health and safety at work regulations. Some occupations are more healthy by their very nature e.g. bus drivers have a sedentary and stressful occupation while bus conductors are more active and less stressed. Some work environments e.g. pubs, give exposure to a less healthy lifestyle. Some occupations by their very nature attract more healthy workers. This may be accentuated by health checks made on appointment or by the need to pass regular health checks e.g. airline pilots. Some occupations can attract less healthy workers, for example, former miners who have left the mining industry as a result of ill health and then chosen to sell newspapers. This will inflate the mortality rates of newspaper sellers. A person s occupation largely determines their income, which permits them to adopt a particular lifestyle e.g. content and pattern of diet, quality of housing. This effect can be positive or negative e.g. over-indulgence. Other appropriate examples were credited. 3 As t increases, t increases, but t p 0 decreases. At t = 80 approximately, the decrease in t p 0 is greater than the increase in t, hence f0 t t p 0 t decreases. A deceptively straightforward answer which many students struggled to find. The key point is to compare the 2 parameters as shown. Page 2

32 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report p p45.5 * p46 * 0.25 p47 1 q q 45 *(1 q )*( q ) *( )*(1 0.25* ) 1 0.5* * * (a) The required probability is dt e 1 e (b) The curtate expectation is k dt k e k p20 e e k 1 k 1 k 1 1 e (12) ä is the present value of 1 p.a. payable monthly in advance while two lives 60:50:20 aged 60 and 50 are both still alive, for a maximum period of 20 years. (12) (12) 20 (12) 60:50:20 60: :50 80:70 ä ä v p ä 20 ( a 11 60:50 ) v p60:50 ( a80:70 ) ( ) v ( ) Page 3

33 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report t 1 0 t t 1 20 t 0 u 21 t hh ss t u ss 7 EPV = 10,000 p * * p * e p du dt where is the force of interest t 20 hh p is the probability of a healthy life aged 20 being healthy at age 20 t 1 p20 ss t is the probability that a life who is sick at age 20 t is sick continuously for one year thereafter u 21 ss t p is the probability that a life who is sick at age 21 t is still sick at age 21 t u This question was not done well and few students obtained the whole result. Partial credits were given for correct portions. There were other potentially correct approaches which were credited provided proper definitions of symbols given. 8 Premium = 20, 000 D 10, l D l D a a a a D65 l65 D62 l65 D62 a 12 5 D D v a l l a D D v ) 67 70:67 a a a ( ) ( ) Premium = 265, , = 300,308 to nearer Page 4

34 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report 9 (i) 10, 000a A B max K60 1, K60 1 and P is the single premium. P, where A and B refer to the first and second lives A B A B (ii) P 10, 000 a60 a60 a60 * a 60 10,000* ,940 Variance = 10 d A 2 A B A A B 60 :60 60 : * * * standard deviation = 22, (i) The gross future loss random variable is 100,000 1 T20 T K20 1 K20 1 bk v I ea fv Ga where b is the annual rate of bonus I is the initial expense e is the annual renewal expense and f is the claim expense G is the gross annual premium (ii) The premium is given by Ga 20,000A 20 3,000 IA Ga G * ,000 *1.06 * ,000 *1.06 * G *( ) 1] G G Page 5

35 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report (iii) The required provision is 110,000A a 23 4,000 IA * * ,000 *1.04 * *684.49* ,000* * , , , , Unit fund Year Fund at the start of the year Premium Allocation to units Interest Management charge Fund at the end of the year Non-unit fund before provisions Year Premium margin Expenses Interest Death cost Maturity cost Management charge Profit Provision required at the start of year 3 = ( (1 p 64 )) / 1.04 = Reduced profit at the end of year 2 = *p 63 = Page 6

36 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report Revised profit vector: , ,0 p p * p62 Net Present Value = p62 2 p62 Present value of premiums = 10000* Profit margin = % Most students completed the tables satisfactorily in this question but struggled to get the revised profit vectors. Very few produced a complete result. 12 (i) Let P be the annual premium. 0.95* P* a * A m f m f 50 :50 50 :50 a a a a m f 50 :50 m f m f : m f m f m f 50 :50 50 :50 50 :50 A 1.04 * A 1.04 *(1 d * a ) *( *20.694) * P* * P 2, (ii) From part (i) the net premium is: * (1.04) * a 1 m f 50 :50 d at 4% = * (1.04) * = We require 3 provisions at end of 5 th policy year Page 7

37 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report Both lives alive * (1.04) * 1 a 0.5 m f 55 :55 a m f 50 :50 = * (1.04) = Male only alive A a m m = * (1.04) * 1 * * = Female only alive A a f f = * (1.04) * 1 * * = Mortality Profit Loss = Expected Death Strain Actual Death Strain In this case there are 4 components: (a) Both lives die during 2004 no actual claims Result = 0.5 (4900 * q m * q f 0)( * ) = (4900 * * ) ( ) = (b) Female alive at begin 2004, death during actual claim Result = 0.5 (100 * q f 1)( * ) 54 Page 8

38 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report = (100 * ) ( ) = (c) Both lives alive beginning 2004, males only die during actual claim. Here the claim cost is the change in provision from joint lives to female only surviving i.e. Result = (4900 * q * q 1)( ) m f = (4900 * * ) ( ) = (d) Both lives alive beginning 2004, females only die during 2004 no actual claims. Claim cost change in provision from joint lives to male only surviving Result = (4900 * p * q 0)( ) m f = (4900 * * ) ( ) = Hence overall total = = i.e. a mortality loss of when rounded. For part (i) assuming renewal expenses did not include the first premium (answer ) was also fully acceptable. Part (ii) was very challenging and very few students realised the extension of mortality profit/loss extended to joint life contracts involved reserve change costs on first death. Most just considered the first 2 components of the answer and in many cases failed to correctly cost this part. A few exceptional students did manage to reach the final result. 13 (i) Define a service table: l 26 t = no. of members aged 26 + t last birthday r 26 t = no. of members who retire age 26 + t last birthday sx t / s x = ratio of earnings in the year of age x + t to x + t + 1 to the earnings in the year of age x to x + 1 Page 9

39 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report 1 r Define z26 t s26 t 3 s26 t 2 s26 t 1 ; a 26 t = value of annuity of 1 p.a. 3 to a retiree aged exactly 26 + t. Past service: Assume that retirements take place uniformly over the year of age between 60 and 65. Retirement for those who attain age 65 takes place at exact age 65. Consider retirement between ages 26 + t and 26 + t + 1, 34 t 38. The present value of the retirement benefits related to past service: 50000*5 z r 50000*5 C t 2 z ra 26 t v 26 t r 26 t a t s 2 s v l26 D26 where z ra 26 t 1 2 r C26 t z26 t 1 v r26 ta t 2 and s 26 D26 s25.25v l 26 For retirement at age 65, the present value of the benefits is: z 65 z ra 65 v r 65 r 65 a C s v l26 D * *5 60 s 60 where z ra 65 r C65 z65v r65 a 65 Summing over all ages, the value is: 50000*5 60 z s M D ra where 39 z ra z ra M60 C26 t t 34 Future service: Assume that retirements take place uniformly over the year of age, between ages 60 and 65. Retirement at 65 takes place at exactly age 65. If retirement takes place between ages 60 and 61, the number of future years service to count is 34. If retirement takes place at age 61 or after, the number of future years service to count is 35. For retirement between ages 60 and 61, the present value of the retirement benefits is: Page 10

40 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report 34*50000 z r 34*50000 C 60 s z ra 60 v 60 i 60 a s v l26 D26 For retirement at later years, the formula is similar to the above, with 35 in place of 34. Adding all these together gives: z ra 60 35( z ra z ra C C C s 65 ) 60 D z ra = M s D 26 where z 5 M60 ra 35* z C60 ra t z C60 ra t 0 (ii) Define a service table, with l 26 t and sx t / s x defined as in part (i). In addition, define d 26 t as the number of members dying age 26 t last birthday. Assume that deaths take place on average in the middle of the year of age. The present value of the death benefit, for death between ages t 1, is t and 26 t t v 26 t s 26 d t s 26 s v l26 D * 4* s d 50000* 4* C where s d 26 t 1 C 2 26 t s26.25 t v d26 t Adding the present value of benefits for all possible years of death gives 38 s C26 d t s M 26 d s s t 0 D26 D * 4* * where 38 s d s d M 26 C26 t t 0 Examiners felt that this question was quite simple provided students constructed proper definitions and followed them through logically allowing of course for the adjusted salary scale. The above answer is one of a number possible and full credit was given for credible alternatives. Page 11

41 Subject CT5 (Contingencies Core Technical) September 2005 Examiners Report Many students, however struggled with this question despite these remarks. END OF EXAMINERS REPORT Page 12

43 1 It is possible to model the mortality of current active members of a pension scheme using the following three-state continuous-time Markov model, with age-dependent forces of transition x, x and x : x Active Retired x x Dead A pension scheme provides a benefit of 10,000 payable on death regardless of whether death occurs before or after retirement. Give an expression to value this benefit for an active life currently aged x. [2] 2 (i) In the context of with-profit policies, describe the super compound method of adding bonuses. [2] (ii) Suggest a reason why a life insurance company might use the super compound method of adding bonuses as opposed to the compound method. [1] [Total 3] 3 Using the PMA92C20 table for both lives calculate: (a) 65:60 (b) 5 p 65:60 (c) 1 2q 65:65 [4] 4 State the main difference between an overhead expense and a direct expense incurred in writing a life insurance policy and give an example of each. [4] CT5 A2006 2

44 5 A life office issues term assurance policies to 500 lives all aged 30 exact with a term of 25 years. The benefit of 10,000 is payable at the end of the year of death of any of the lives into a special fund. Calculate the expected share of this fund for each survivor after 25 years. Basis: Mortality Interest AM92 Select 4% per annum [4] 6 A life office has issued for a number of years whole-life regular premium policies to a group of lives through direct advertising. Assured lives are only required to complete an application form with no further evidence of health. Outline the forms of selection that the insurer should expect to find in the mortality experience of the lives. [5] 7 (i) Show that: t p p ( ) s x t s x t x t x t s [2] (ii) Prove Thiele s differential equation for a whole-life assurance issued to a life aged x to be as follows: t V (1 V ) V Px t x t x x t t x [4] [Total 6] 8 (i) Calculate the expected present value of an annuity-due of 1 per annum payable annually in advance until the death of the last survivor of two lives using the following basis: First life: male aged 70, mortality table PMA92C20 Second life: female aged 67, mortality table PFA92C20 Rate of interest: 4% per annum [2] (ii) Give an expression for the variance of the annuity-due in terms of annuity functions. [5] [Total 7] CT5 A PLEASE TURN OVER

45 9 (i) Express fully in words: a [3] xy: n (ii) Express a as the expected value of random variables and hence show that xy: n a xy: n 1 A xy: n [4] [Total 7] 10 A 20-year special endowment assurance policy is issued to a group of lives aged 45 exact. Each policy provides a sum assured of 10,000 payable at the end of the year of death or 20,000 payable if the life survives until the maturity date. Premiums on the policy are payable annually in advance for 15 years or until earlier death. You are given the following information: Number of deaths during the 13 th policy year 4 Number of policies in force at the end of the 13 th policy year 195 (i) Calculate the profit or loss arising from mortality in the 13 th policy year. [7] (ii) Comment on your results. [2] Basis: Mortality Interest Expenses AM92 Ultimate 4% per annum none [Total 9] 11 An employer wishes to introduce a lump-sum retirement benefit payable immediately on retirement at 65 or earlier other than on the grounds of ill-health. The amount of the benefit is 1,000 for each year of an employee s service, with proportionate parts of a year counting. (i) (ii) (iii) Give a formula to value this benefit for an employee currently aged x with n years of past service, defining all terms used. [5] Using the Pension Scheme Tables from the Actuarial Formulae and Tables, calculate the value for an employee currently aged 30 exact with exactly 10 years past service. [2] Calculate the level annual contribution payable continuously throughout this employee s service to fund the future retirement benefit. [3] [Total 10] CT5 A2006 4

46 12 (i) Define the following terms without giving detailed formulae: (a) (b) (c) Crude Mortality Rate Directly Standardised Mortality Rate Indirectly Standardised Mortality Rate [3] (ii) The data in the following table are taken from data published by the Office of National Statistics in England and Wales Population Number of births Tyne and Wear Population Number of births Under 25 3,149, ,000 71,000 4, ,769, ,000 74,000 6, ,927, ,000 82,000 1,000 (a) (b) Using the population for England and Wales as the standard population calculate crude birth rates and the directly and indirectly standardised birth rates for Tyne and Wear. State an advantage of using the Indirectly Standardised Birth Rate and comment briefly on the answers you have obtained. [8] [Total 11] CT5 A PLEASE TURN OVER

### INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION

INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 27 April 2015 (pm) Subject CT5 Contingencies Core Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and examination

### INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 8 October 2015 (pm) Subject CT5 Contingencies Core Technical

### INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 17 th November 2011 Subject CT5 General Insurance, Life and Health Contingencies Time allowed: Three Hours (10.00 13.00 Hrs) Total Marks: 100 INSTRUCTIONS TO

### INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 13 th May 2015 Subject CT5 General Insurance, Life and Health Contingencies Time allowed: Three Hours (10.30 13.30 Hrs) Total Marks: 100 INSTRUCTIONS TO THE

### Heriot-Watt University. BSc in Actuarial Mathematics and Statistics. Life Insurance Mathematics I. Extra Problems: Multiple Choice

Heriot-Watt University BSc in Actuarial Mathematics and Statistics Life Insurance Mathematics I Extra Problems: Multiple Choice These problems have been taken from Faculty and Institute of Actuaries exams.

### O MIA-009 (F2F) : GENERAL INSURANCE, LIFE AND

No. of Printed Pages : 11 MIA-009 (F2F) kr) ki) M.Sc. ACTUARIAL SCIENCE (MSCAS) N December, 2012 0 O MIA-009 (F2F) : GENERAL INSURANCE, LIFE AND HEALTH CONTINGENCIES Time : 3 hours Maximum Marks : 100

### EXAMINATIONS. 18 April 2000 (am) Subject 105 Actuarial Mathematics 1. Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE

Faculty of Actuaries Institute of Actuaries EXAMINATIONS 18 April 2000 (am) Subject 105 Actuarial Mathematics 1 Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Write your surname in full, the

### INSTRUCTIONS TO CANDIDATES

Society of Actuaries Canadian Institute of Actuaries Exam MLC Models for Life Contingencies Friday, October 31, 2014 8:30 a.m. 12:45 p.m. MLC General Instructions 1. Write your candidate number here. Your

### JANUARY 2016 EXAMINATIONS. Life Insurance I

PAPER CODE NO. MATH 273 EXAMINER: Dr. C. Boado-Penas TEL.NO. 44026 DEPARTMENT: Mathematical Sciences JANUARY 2016 EXAMINATIONS Life Insurance I Time allowed: Two and a half hours INSTRUCTIONS TO CANDIDATES:

### SOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS

SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS The following questions or solutions have been modified since this document was prepared to use with the syllabus effective

### Solution. Let us write s for the policy year. Then the mortality rate during year s is q 30+s 1. q 30+s 1

Solutions to the May 213 Course MLC Examination by Krzysztof Ostaszewski, http://wwwkrzysionet, krzysio@krzysionet Copyright 213 by Krzysztof Ostaszewski All rights reserved No reproduction in any form

### November 2012 Course MLC Examination, Problem No. 1 For two lives, (80) and (90), with independent future lifetimes, you are given: k p 80+k

Solutions to the November 202 Course MLC Examination by Krzysztof Ostaszewski, http://www.krzysio.net, krzysio@krzysio.net Copyright 202 by Krzysztof Ostaszewski All rights reserved. No reproduction in

### SOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE WRITTEN-ANSWER QUESTIONS AND SOLUTIONS

SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE WRITTEN-ANSWER QUESTIONS AND SOLUTIONS Questions February 12, 2015 In Questions 12, 13, and 19, the wording was changed slightly

### May 2012 Course MLC Examination, Problem No. 1 For a 2-year select and ultimate mortality model, you are given:

Solutions to the May 2012 Course MLC Examination by Krzysztof Ostaszewski, http://www.krzysio.net, krzysio@krzysio.net Copyright 2012 by Krzysztof Ostaszewski All rights reserved. No reproduction in any

### Chapter 2. 1. You are given: 1 t. Calculate: f. Pr[ T0

Chapter 2 1. You are given: 1 5 t F0 ( t) 1 1,0 t 125 125 Calculate: a. S () t 0 b. Pr[ T0 t] c. Pr[ T0 t] d. S () t e. Probability that a newborn will live to age 25. f. Probability that a person age

### SOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS

SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS The following questions or solutions have been modified since this document was prepared to use with the syllabus effective

### Some Observations on Variance and Risk

Some Observations on Variance and Risk 1 Introduction By K.K.Dharni Pradip Kumar 1.1 In most actuarial contexts some or all of the cash flows in a contract are uncertain and depend on the death or survival

### TABLE OF CONTENTS. GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL

TABLE OF CONTENTS GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL CHAPTER ONE: REVIEW OF INTEREST THEORY 3 1.1 Interest Measures 3 1.2 Level Annuity

### 1 Cash-flows, discounting, interest rate models

Assignment 1 BS4a Actuarial Science Oxford MT 2014 1 1 Cash-flows, discounting, interest rate models Please hand in your answers to questions 3, 4, 5 and 8 for marking. The rest are for further practice.

### EXAMINATION. 22 April 2010 (pm) Subject ST2 Life Insurance Specialist Technical. Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE

Faculty of Actuaries Institute of Actuaries EXAMINATION 22 April 2010 (pm) Subject ST2 Life Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate

### MINIMUM SURRENDER VALUES AND PAID-UP VALUES

MARCH 2002 Actuarial Standard 4.02 MINIMUM SURRENDER VALUES AND PAID-UP VALUES Life Insurance Actuarial Standards Board TABLE OF CONTENTS INTRODUCTION PAGE The Standard 2 Application of the Surrender Value

### Abbey Life Assurance Company Limited Participating Business Fund

Abbey Life Assurance Company Limited Participating Business Fund Principles and of Financial Management (PPFM) 1 General... 2 1.1 Introduction... 2 1.2 The With-Profits Policies... 2 2 Structure of these

### PREMIUM AND BONUS. MODULE - 3 Practice of Life Insurance. Notes

4 PREMIUM AND BONUS 4.0 INTRODUCTION A insurance policy needs to be bought. This comes at a price which is known as premium. Premium is the consideration for covering of the risk of the insured. The insured

### Actuarial Society of India

Actuarial Society of India EXAMINATION 30 th October 2006 Subject ST1 Health and Care Insurance Specialist Technical Time allowed: Three hours (14.15* pm 17.30 pm) INSTRUCTIONS TO THE CANDIDATE 1. Enter

### Broker Guide to Canada Life Products Version 42

This document is intended for Financial Advisors only and not consumers. Broker Guide to Canada Life Products Version 42 SOURCE: Marketing Information valid as per April 2013 This Guide does not form part

### LIFE INSURANCE. and INVESTMENT

INVESTMENT SAVINGS & INSURANCE ASSOCIATION OF NZ INC GLOSSARY OF LIFE INSURANCE and INVESTMENT TERMS 2 Accident Benefit A benefit payable should death occur as the result of an accident. It may be a stand-alone

### Note: The paid up value would be payable only on due maturity of the policy.

Section II Question 6 The earning member of a family aged 35 years expects to earn till next 25 years. He expects an annual growth of 8% in his existing net income of Rs. 5 lakh p.a. If he considers an

### Valuation Report on Prudential Annuities Limited as at 31 December 2003. The investigation relates to 31 December 2003.

PRUDENTIAL ANNUITIES LIMITED Returns for the year ended 31 December 2003 SCHEDULE 4 Valuation Report on Prudential Annuities Limited as at 31 December 2003 1. Date of investigation The investigation relates

### Glossary of insurance terms

Glossary of insurance terms I. Insurance Products Annuity is a life insurance policy where an insurance company pays an income stream to an individual, usually until death, in exchange for the payment

### Premium calculation. summer semester 2013/2014. Technical University of Ostrava Faculty of Economics department of Finance

Technical University of Ostrava Faculty of Economics department of Finance summer semester 2013/2014 Content 1 Fundamentals Insurer s expenses 2 Equivalence principles Calculation principles 3 Equivalence

### 2 Policy Values and Reserves

2 Policy Values and Reserves [Handout to accompany this section: reprint of Life Insurance, from The Encyclopaedia of Actuarial Science, John Wiley, Chichester, 2004.] 2.1 The Life Office s Balance Sheet

### INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION

INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 30 April 2015 (am) Subject SA2 Life Insurance Specialist Applications Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and

### Life Assurance (Provision of Information) Regulations, 2001

ACTUARIAL STANDARD OF PRACTICE LA-8 LIFE ASSURANCE PRODUCT INFORMATION Classification Mandatory MEMBERS ARE REMINDED THAT THEY MUST ALWAYS COMPLY WITH THE CODE OF PROFESSIONAL CONDUCT AND THAT ACTUARIAL

### Premium Calculation. Lecture: Weeks 12-14. Lecture: Weeks 12-14 (Math 3630) Annuities Fall 2015 - Valdez 1 / 32

Premium Calculation Lecture: Weeks 12-14 Lecture: Weeks 12-14 (Math 3630) Annuities Fall 2015 - Valdez 1 / 32 Preliminaries Preliminaries An insurance policy (life insurance or life annuity) is funded

### Windsor Life Assurance Company Limited. Windsor Life With-Profit Fund. Principles and Practices of Financial Management

Windsor Life Assurance Company Limited Windsor Life With-Profit Fund Principles and Practices of Financial Management July 2011 Registered in England No. 754167. Registered Office: Windsor House, Telford

### Annuities and decumulation phase of retirement. Chris Daykin UK Government Actuary Chairman, PBSS Section of IAA

Annuities and decumulation phase of retirement Chris Daykin UK Government Actuary Chairman, PBSS Section of IAA CASH LUMP SUM AT RETIREMENT CASH INSTEAD OF PENSION > popular with pension scheme members

### GROUP INCOME PROTECTION

GROUP INCOME PROTECTION PROACTIVE PROTECTION PROVIDED BY METLIFE POLICY technical guide This document is a guide to the features, benefits, risks and limitations of the policy, including how the policy

### Heriot-Watt University. M.Sc. in Actuarial Science. Life Insurance Mathematics I. Tutorial 5

1 Heriot-Watt University M.Sc. in Actuarial Science Life Insurance Mathematics I Tutorial 5 1. Consider the illness-death model in Figure 1. A life age takes out a policy with a term of n years that pays

### MONEY BACK PLANS. For the year 2004-05 the two rates of investment return declared by the Life Insurance Council are 6% and 10% per annum.

MONEY BACK PLANS 1. Money Back with Profit Unlike ordinary endowment insurance plans where the survival benefits are payable only at the end of the endowment period, this scheme provides for periodic payments

### Further Topics in Actuarial Mathematics: Premium Reserves. Matthew Mikola

Further Topics in Actuarial Mathematics: Premium Reserves Matthew Mikola April 26, 2007 Contents 1 Introduction 1 1.1 Expected Loss...................................... 2 1.2 An Overview of the Project...............................

### Unit-Linked Insurance Policies in the Indian Market- A Consumer Perspective

Unit-Linked Insurance Policies in the Indian Market- A Consumer Perspective R. Rajagopalan 1 Dean (Academic Affairs) T.A. Pai Management Institute Manipal-576 104 Email: raja@mail.tapmi.org 1 The author

### Scottish Friendly Assurance Society Limited

Scottish Friendly Assurance Society Limited Principles and Practices of Financial Management for With-Profits Business Transferred from Scottish Legal Life Scottish Friendly Assurance Society Limited Principles

### Premium Calculation. Lecture: Weeks 12-14. Lecture: Weeks 12-14 (STT 455) Premium Calculation Fall 2014 - Valdez 1 / 31

Premium Calculation Lecture: Weeks 12-14 Lecture: Weeks 12-14 (STT 455) Premium Calculation Fall 2014 - Valdez 1 / 31 Preliminaries Preliminaries An insurance policy (life insurance or life annuity) is

### POLICE MUTUAL ASSURANCE SOCIETY. Principles and Practices of Financial Management July 2015. PPFM v16.4

PPFM v16.4 1. INTRODUCTION... 1 1.1. Purpose and History... 1 1.2. Fair and effective management... 2 1.2. Overview... 3 1.3. Principles of Financial Management... 4 1.4. Practices of Financial Management...

### INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 15 th November 2010 Subject CT1 Financial Mathematics Time allowed: Three Hours (15.00 18.00 Hrs) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1. Please

### ACTUARIAL MATHEMATICS FOR LIFE CONTINGENT RISKS

ACTUARIAL MATHEMATICS FOR LIFE CONTINGENT RISKS DAVID C. M. DICKSON University of Melbourne MARY R. HARDY University of Waterloo, Ontario V HOWARD R. WATERS Heriot-Watt University, Edinburgh CAMBRIDGE

### THE XYZ Pension and Life Assurance Scheme. Members Booklet January 2014 Edition. For Employees of the XYZ Company

THE XYZ Pension and Life Assurance Scheme Members Booklet January 2014 Edition For Employees of the XYZ Company Reviewed January 2014 CONTENTS Page 3 INTRODUCTION 4 TERMS USED IN THIS BOOKLET 7 GENERAL

### A chapter on Valuation basis covering the following minimum criteria should also be displayed on the web-site of the Insurers.

L-42 42- Valuation Basis (Life Insurance) A chapter on Valuation basis covering the following minimum criteria should also be displayed on the web-site of the Insurers. Data The company maintains the Policy

### National specific template Log NS.09 best estimate assumptions for life insurance risks

National specific template Log NS.09 best estimate assumptions for life insurance risks CELL(S) ITEM INSTRUCTIONS N/A General Comment This template is applicable to life insurers and life reinsurers. The

### The Lafayette Life Insurance Company Agents Products Quiz The Marquis Series of Products and Other Annuities

There are different types of annuity products that can serve different needs. Even within a particular type of annuity product category, for example a fixed indexed annuity, the benefits and features can

### NORTH CAROLINA GENERAL ASSEMBLY 1981 SESSION CHAPTER 761 SENATE BILL 623

NORTH CAROLINA GENERAL ASSEMBLY 1981 SESSION CHAPTER 761 SENATE BILL 623 AN ACT TO AMEND CHAPTER 58, ARTICLE 22, OF THE GENERAL STATUTES RELATING TO NONFORFEITURE BENEFITS OF LIFE INSURANCE POLICIES AND

### Practice Exam 1. x l x d x 50 1000 20 51 52 35 53 37

Practice Eam. You are given: (i) The following life table. (ii) 2q 52.758. l d 5 2 5 52 35 53 37 Determine d 5. (A) 2 (B) 2 (C) 22 (D) 24 (E) 26 2. For a Continuing Care Retirement Community, you are given

### An Adviser s Guide to Pensions

An Adviser s Guide to Pensions 1 An Adviser s Guide to Pensions Contents: Section 1: Personal Pensions 1.1 Eligibility 1.2 Maximum Benefits 1.3 Contributions & Tax Relief 1.4 Death Benefits 1.5 Retirement

### Income Protection. Karen Gallagher Business Development Manager

Karen Gallagher Business Development Manager THE NEED FOR INCOME PROTECTION Worker s confusion over sick pay 30% of workers believe their employer will provide sick pay indefinitely Over- optimism re:

### Please write your name and student number at the spaces provided:

MATH 3630 Actuarial Mathematics I Final Examination - sec 001 Monday, 10 December 2012 Time Allowed: 2 hours (6:00-8:00 pm) Room: MSB 411 Total Marks: 120 points Please write your name and student number

### International Accounting Standard 19 Employee Benefits

International Accounting Standard 19 Employee Benefits Objective The objective of this Standard is to prescribe the accounting and disclosure for employee benefits. The Standard requires an entity to recognise:

### FLEXIBLE LIFETIME ANNUITY NATIONAL INSURANCE NUMBER POLICY NUMBER

FLEXIBLE LIFETIME ANNUITY NATIONAL INSURANCE NUMBER POLICY NUMBER 1 THE PRUDENTIAL ASSURANCE COMPANY LIMITED Incorporated in England Reg'd No. 15454 Registered Office: Laurence Pountney Hill, London, EC4R

### IndiaFirst Money Back Health Insurance Plan Vs IndiaFirst Secure Save Plan

Vs Hospitalisation Benefit 1. Hospitalization of insured is covered up to 1 % of the annual Sum Insured, maximum of Rs. 5000/ per day. 2. Room, boarding and nursing expenses as charged by the hospital

### 58-58-50. Standard Valuation Law.

58-58-50. Standard Valuation Law. (a) This section shall be known as the Standard Valuation Law. (b) Each year the Commissioner shall value or cause to be valued the reserve liabilities ("reserves") for

### THE MATHEMATICS OF LIFE INSURANCE THE NET SINGLE PREMIUM. - Investigate the component parts of the life insurance premium.

THE MATHEMATICS OF LIFE INSURANCE THE NET SINGLE PREMIUM CHAPTER OBJECTIVES - Discuss the importance of life insurance mathematics. - Investigate the component parts of the life insurance premium. - Demonstrate

### INSURANCE DEPARTMENT OF THE STATE OF NEW YORK REGULATION NO. 147 (11 NYCRR 98) VALUATION OF LIFE INSURANCE RESERVES

INSURANCE DEPARTMENT OF THE STATE OF NEW YORK REGULATION NO. 147 (11 NYCRR 98) VALUATION OF LIFE INSURANCE RESERVES I, Gregory V. Serio, Superintendent of Insurance of the State of New York, pursuant to

### 6 Insurances on Joint Lives

6 Insurances on Joint Lives 6.1 Introduction Itiscommonforlifeinsurancepoliciesandannuitiestodependonthedeathorsurvivalof more than one life. For example: (i) Apolicywhichpaysamonthlybenefittoawifeorotherdependentsafterthedeathof

### Termination Values, Minimum Surrender Values and Paid-up Values

Prudential Standard LPS 360 Termination Values, Minimum Surrender Values and Paid-up Values Objective and key requirements of this Prudential Standard This Prudential Standard sets out the requirements

### Buying a pension annuity

Buying a pension annuity Why do I need to think about buying a pension annuity? When you come to retire, you will have some important decisions to make. Probably most important of all is how you will generate

### B1.03: TERM ASSURANCE

B1.03: TERM ASSURANCE SYLLABUS Term assurance Increasing term assurance Decreasing term assurance Mortgage protection Renewable and convertible term assurance Pension term assurance Tax treatment Family

### Group Income Protection Technical Guide

For commercial customers and their advisers only Group Income Protection Technical Guide Reference BGR/4019/OCT12 Contents Page Its aims Employers your commitment Risk factors How does the policy work?

### Finance 160:163 Sample Exam Questions Spring 2003

Finance 160:163 Sample Exam Questions Spring 2003 These questions are designed to test your understanding of insurance operations within the context of life and health insurance. Each question is given

### Manual for SOA Exam MLC.

Chapter 6. Benefit premiums Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/90 (#4, Exam M, Spring 2005) For a fully discrete whole life insurance of 100,000 on (35)

### No. 63 Page 1 of 71 2015

No. 63 Page 1 of 71 No. 63. An act relating to principle-based valuation for life insurance reserves and a standard nonforfeiture law for life insurance policies. (H.482) It is hereby enacted by the General

### GN8: Additional Guidance on valuation of long-term insurance business

GN8: Additional Guidance on valuation of long-term insurance business Classification Practice Standard MEMBERS ARE REMINDED THAT THEY MUST ALWAYS COMPLY WITH THE PROFESSIONAL CONDUCT STANDARDS (PCS) AND

### - LIFE INSURANCE CORPORATION OF INDIA CENTRAL OFFICE. Dept.: Product Development Jeevan Bima Marg, Mumbai 400 021

- LIFE INSURANCE CORPORATION OF INDIA CENTRAL OFFICE Dept.: Product Development Yogakshema, Jeevan Bima Marg, Mumbai 400 021 Ref: CO/PD/66 3 rd March, 2015 All HODs of Central Office All Zonal Offices

### Income Protection. The Income Protection Market - Opportunity? Karen Gallagher Business Development Manager

Karen Gallagher Business Development Manager The Market - Opportunity? Only 12% to 15% of the working population have cover Majority of people in Ireland are still in employment Current consumer sentiment

### Agenda. Session 3: GAAP for Traditional Non-Par Products SFAS 60 and SFAS 97 Limited Pay. Amsterdam 2007 Tom Herget PolySystems, Inc.

Session 3: GAAP for Traditional Non-Par Products SFAS 60 and SFAS 97 Limited Pay Amsterdam 2007 Tom Herget PolySystems, Inc. Agenda Overview Long Duration Contracts Benefit Reserves Deferred Policy Acquisition

### FACTS AND FEATURES SIDE BY SIDE.

INCOME PROTECTION BENEFIT PLAN (IPB) AND FACTS AND FEATURES SIDE BY SIDE. It s our aim to make selling income protection as simple as possible. Here, we ve compared the features of our Income Protection

### THE HALIFAX RETIREMENT FUND MEMBERS' GUIDE

THE HALIFAX RETIREMENT FUND MEMBERS' GUIDE CONTENTS 1 Definitions 2 Membership 3 Contributions 4 Additional voluntary contributions (AVCs) 5 Tax relief 6 Retirement Benefits (including taking benefits

### Institute of Actuaries of India

Institute of Actuaries of India GUIDANCE NOTE (GN) 6: Management of participating life insurance business with reference to distribution of surplus Classification: Recommended Practice Compliance: Members

### SECTION 99.1 Purposes. The purposes of this Part are:

INSURANCE DEPARTMENT OF THE STATE OF NEW YORK REGULATION NO. 151 (11 NYCRR 99) VALUATION OF ANNUITY, SINGLE PREMIUM LIFE INSURANCE, GUARANTEED INTEREST CONTRACT AND OTHER DEPOSIT RESERVES I, Neil D. Levin,

### HOW WE MANAGE THE PHOENIX LIFE LIMITED PHOENIX WITH-PROFITS FUND

HOW WE MANAGE THE PHOENIX LIFE LIMITED PHOENIX WITH-PROFITS FUND A guide for policyholders with unitised with-profits policies (except for Profit Plus Fund policies) invested in this fund The aims of this

### A chapter on Valuation basis covering the following minimum criteria should also be displayed on the web-site of the Insurers.

L-42 42- Valuation Basis (Life Insurance) A chapter on Valuation basis covering the following minimum criteria should also be displayed on the web-site of the Insurers. Data The company maintains the Policy

### International Bond Key features

International Bond Key features This is an important document. Please read it and keep for future reference. Helping you decide This key features document contains important information about the main

### WHAT IS LIFE INSURANCE?

UNDERSTANDING LIFE INSURANCE Presented by The Kansas Insurance Department WHAT IS LIFE INSURANCE? a. Insurance Contract issued by an Insurance Company. b. Premiums paid under the contract provide for a

### VERMONT DEPARTMENT OF BANKING AND INSURANCE REVISED REGULATION 77-2 VERMONT LIFE INSURANCE SOLICITATION REGULATION

VERMONT DEPARTMENT OF BANKING AND INSURANCE REVISED REGULATION 77-2 VERMONT LIFE INSURANCE SOLICITATION REGULATION Section 1. AUTHORITY This rule is adopted and promulgated by the Commissioner of Banking

### THE XYZ Pension and Life Assurance Scheme. Members Booklet April 2015 Edition. For Employees of the XYZ Company

THE XYZ Pension and Life Assurance Scheme Members Booklet April 2015 Edition For Employees of the XYZ Company Reviewed May 2015 1 CONTENTS Page 3 INTRODUCTION 4 TERMS USED IN THIS BOOKLET 8 GENERAL 9 CONTRIBUTIONS

### Birla Sun Life Insurance Dream Endowment Plan. Birla Sun Life Insurance Company Limited

Birla Sun Life Insurance Dream Endowment Plan Copyright 2008 Investment risk in the investment portfolio is borne by the policy holder. The premiums paid in Unit Linked Life Insurance policies are subject

### OBJECTIVE SCOPE Paragraphs 1 6 DEFINITIONS 7 SHORT-TERM EMPLOYEE BENEFITS 8 23 Recognition and Measurement 10 22

160 Accounting Standard (AS) 15 Employee Benefits Contents OBJECTIVE SCOPE Paragraphs 1 6 DEFINITIONS 7 SHORT-TERM EMPLOYEE BENEFITS 8 23 Recognition and Measurement 10 22 All Short-term Employee Benefits

### 1. Introduction. 1.1 Objective

Second International Comparative Study of Mortality Tables for Pension Fund Retirees T.Z.Sithole (Kingston University London), S.Haberman (Cass Business School, City University London) and R.J.Verrall

### Annuities. Lecture: Weeks 9-11. Lecture: Weeks 9-11 (STT 455) Annuities Fall 2014 - Valdez 1 / 43

Annuities Lecture: Weeks 9-11 Lecture: Weeks 9-11 (STT 455) Annuities Fall 2014 - Valdez 1 / 43 What are annuities? What are annuities? An annuity is a series of payments that could vary according to:

### TRANSACTIONS OF SOCIETY OF ACTUARIES 1952 VOL. 4 NO. 10 COMPLETE ANNUITIES. EUGENE A. RASOR* Ann T. N. E. GREVILLE

TRANSACTIONS OF SOCIETY OF ACTUARIES 1952 VOL. 4 NO. 10 COMPLETE ANNUITIES EUGENE A. RASOR* Ann T. N. E. GREVILLE INTRODUCTION I N GENERAL, a complete annuity of one per annum may be defined as a curtate

### SURRENDER VALUE AND PAID-UP VALUE STANDARD FOR LIFE INSURANCE

Actuarial Society of Malaysia (ASM) SURRENDER VALUE AND PAID-UP VALUE STANDARD FOR LIFE INSURANCE Prepared by: Life Insurance Sub-Committee of Actuarial Society of Malaysia TABLE OF CONTENTS CONTENTS PAGE

### FINANCIAL ANALYSIS ****** UPDATED FOR 55% BENEFIT ****** ****** FOR ALL SURVIVORS ******

FINANCIAL ANALYSIS ****** UPDATED FOR 55% BENEFIT ****** ****** FOR ALL SURVIVORS ****** This fact sheet is designed to supplement the Department of Defense brochure: SBP SURVIVOR BENEFIT PLAN FOR THE

### This guide is for you, if you have a traditional with-profits pension policy with either

This guide is for you, if you have a traditional with-profits pension policy with either Guardian Assurance Ltd or Countrywide Assured 1 of 15 CONTENTS 1 What is this guide for? 2 Background to Guardian

### Immediate Annuities. Reno J. Frazzitta Investment Advisor Representative 877-909-7233 www.thesmartmoneyguy.com

Reno J. Frazzitta Investment Advisor Representative 877-909-7233 www.thesmartmoneyguy.com Immediate Annuities Page 1 of 7, see disclaimer on final page Immediate Annuities What is an immediate annuity?

### International Accounting Standard 19 Employee Benefits. Objective. Scope IAS 19

International Accounting Standard 19 Employee Benefits Objective 1 The objective of this Standard is to prescribe the accounting and disclosure for employee benefits. The Standard requires an entity to

### METLIFE EXCEPTED GROUP LIFE POLICY TECHNICAL GUIDE

METLIFE EXCEPTED GROUP LIFE POLICY TECHNICAL GUIDE This document is a guide to the features, benefits, risks and limitations of the MetLife Excepted Group Life policy, including how the policy works and

### County of Santa Clara Physicians Faculty & Staff

LONG TERM DISABILITY INCOME PLAN UNDERWRITTEN BY: LIFE INSURANCE COMPANY OF NORTH AMERICA a CIGNA company CLASS 1 1/2004 County of Santa Clara Physicians Faculty & Staff FOREWORD Long Term Disability

### Institute of Actuaries of India Subject ST2 Life Insurance

Institute of Actuaries of India Subject ST2 Life Insurance For 2015 Examinations Aim The aim of the Life Insurance Specialist Technical subject is to instil in successful candidates principles of actuarial

### Guide to Pension Annuities

Guide to Pension Annuities Having successfully built up a pension fund during your working life, there will come a time when you will need to make some important decisions about how to use this fund. These

### DRAFT May 2012. Objective and key requirements of this Prudential Standard

Prudential Standard LPS 340 Valuation of Policy Liabilities Objective and key requirements of this Prudential Standard The ultimate responsibility for the value of a life company s policy liabilities rests