TABLE OF CONTENTS. 4. Daniel Markov 1 173


 Archibald Douglas
 2 years ago
 Views:
Transcription
1 TABLE OF CONTENTS 1. Survival A. Time of Death for a Person Aged x 1 B. Force of Mortality 7 C. Life Tables and the Deterministic Survivorship Group 19 D. Life Table Characteristics: Expectation of Life 27 E. Other Life Table Characteristics 39 F. Different Mortality Rates 47 G. Assumptions for Fractional Ages: Uniform Distribution 53 H. Assumptions for Fractional Ages: Balducci and Constant Force 61 I. De Moivre s Law of Mortality 73 J. Other Laws of Mortality: Gompertz, Makeham, and Weibull Multiple Lives A. Joint Distributions of Future Lifetimes and the Joint Life Status 95 B. The Last Survivor Status 111 C. Expectation and Probabilities Multiple Decrements A. Multiple Random Variables: Basic Probabilities 137 B. Multiple Random Variables: Other Problems 145 C. Random Survivorship Groups: Basic Problems Involving DoubleDecrement Tables Daniel Markov Daniel Poisson A. Definition of a Poisson Process 191 B. Calculating Poisson Probabilities and Moments 193 C. Waiting Times 207 D. Probabilities of Compound Poisson Distributions 213 E. Moments of the Compound Poisson Distribution 219 F. Approximations: Compound Poisson 233 G. Thinning 243 H. Sums of Poisson Processes 253 I. Mixture Distributions: Gamma and Negative Binomials 263 J. Mixture Distributions: Other Distributions 273 K. Nonhomogeneous Poisson Processes 279
2 ii 6. Insurance A. Whole Life and Term Insurance at the Moment of Death: Calculating Expected Values 285 B. Whole Life and Term Insurance at the Moment of Death: Calculating Variances 291 C. Endowment Insurance Payable at the Moment of Death 301 D. Deferred Insurance Payable at the Moment of Death 313 E. Varying Benefit Insurance Payable at the Moment of Death 323 F. Nonvariable Insurance Payable at the End of the Year of Death: Expected Values 331 G. Nonvariable Insurance Payable at the End of the Year of Death: Variances 347 H. Variable Insurance Payable the End of the Year 355 I. Relationships Between Insurances at the Moment of Death and End of the Year of Death Annuities A. Continuous Life Annuities: Expected Values 373 B. Continuous Life Annuities: Other Problems 385 C. Annuities: Calculating Probabilities 395 D. Discrete Whole Life Annuities 405 E. Discrete Temporary Life Annuities 415 F. Deferred Discrete Life Annuities 427 G. Other Discrete Life Annuities 433 H. Reinsurance and Reserves Premiums A. Fully Continuous Level Annual Benefit Premiums 455 B. Fully Continuous Premiums: LossAtIssue Random Variable 463 C. Fully Discrete Level Annual Benefit Premiums 477 D. Fully Discrete Whole Life Premiums: LossAtIssue Random Variable 493 E. Fully Discrete Term and Endowment Premiums: LossatIssue Random Variable 507 F. Semicontinuous, Variable, and Other Premiums Reserves A. Fully Continuous Benefit Reserves: Prospective Formulas 523 B. Fully Continuous Benefit Reserves: Variance of Prospective Loss 533 C. Fully Continuous Benefit Reserves: Retro, PaidUp, and Premium Difference Formulas 537 D. Fully Continuous Benefit Reserves: Special Formulas 543 E. Fully Discrete Benefit Reserves: Prospective Formulas 547 F. Fully Discrete Benefit Reserves: Prospective Loss 559 G. Fully Discrete Benefit Reserves: Retro, PaidUp, and Premium Difference Formulas 569 H. Fully Discrete Benefit Reserves: Special Formulas 581 I. Recursive Relations for Fully Discrete Benefit Reserves Insurances/Annuities A. Multilife Survival Statuses 607 B. Special Annuity Benefits 619 C. Multiple Decrement Insurances and Annuities Daniel Markov 2 659
3 iii 12. Statistics A. Maximum Likelihood Estimation 679 B. MethodofMoments Estimation 713 C. Measures of Quality 729 D. Hypothesis Testing: Normal Distributions 741 E. Hypothesis Testing: Other Questions 759 F. Order Statistics 773 G. The t, F, and ChiSquare Distributions 785 H. LeastSquares Estimation 809 I. Likelihood Ratio Tests 827
4 iv NOTES Questions and parts of some solutions have been taken from material copyrighted by the Casualty Actuarial Society and the Society of Actuaries. They are reproduced in this study manual with the permission of the CAS and SoA solely to aid students studying for the actuarial exams. Some editing of questions has been done. Students may also request past exams directly from both societies. I am very grateful to these organizations for their cooperation and permission to use this material. They are, of course, in no way responsible for the structure or accuracy of the manual. Exam questions are identified by numbers in parentheses at the end of each question. CAS questions have four numbers separated by hyphens: the year of the exam, the number of the exam, the number of the question, and the points assigned. SoA or joint exam questions usually lack the number for points assigned. W indicates a written answer question; for questions of this type, the number of points assigned are also given. A indicates a question from the afternoon part of an exam. MC indicates that a multiple choice question has been converted into a true/false question. Page references refer to Bowers et al., Actuarial Mathematics (1997), Cunningham et al. Models for Quantifying Risk (2008); Daniel, Multistate Transition Models with Actuarial Applications (2007); Daniel Poisson Processes (and mixture distributions) (2008); Hoel, Introduction to Mathematical Statistics (1971), Hogg et al., Introduction to Mathematical Statistics, (2004); Hogg/Tanis, Probability and Statistical Inference (2006): Larsen/Marx, An Introduction to Mathematical Statistics and Its Applications (2006); and Mood, Introduction to the Theory of Statistics (1974). Although I have made a conscientious effort to eliminate mistakes and incorrect answers, I am certain some remain. I am very grateful to students who discovered errors in the past and encourage those of you who find others to bring them to my attention. Please check our web site for corrections subsequent to publication. I would also like to thank Chip Cole, Graham Lord, and Katy Murdza for their help in preparation of the manual. Hanover, NH 7/15/11 PJM
5 Insurance 313 D. Deferred Insurance Payable at the Moment of Death D1. You are given the following for (40): i) Mortality follows de Moivre's law with 100, ii) Z is the present value random variable for a fiveyear deferred life insurance of 1. iii) M is the mode of Z. Which of the following are true? 1. F Z (0) > 0 2. M v 5 3. P(Z < v 30 ).5 A. 1, 2 B. 1,3 C. 2,3 D. 1,2,3 E. None of these answers are correct. (86S 4 21) D2. Z A is the present value random variable for a whole life insurance issued to (x) that pays 2 at the moment of death if death occurs within n years and 1 at the moment of death if death occurs after n years. Z B is the present value random variable for a whole life insurance issued to (x) that pays 1 at the moment of death if death occurs within n years and 2 at the moment of death if death occurs after n years. You are given that E[Z A ] E[Z B ]. a. Write expressions for Z A and Z B in terms of v T where T T(x). b. Determine E[Z A ] in terms of net single premiums. c. Determine E[(Z A ) 2 ] and E[(Z B ) 2 ] in terms of net single premiums. d. Demonstrate that Var(Z A ) Var(Z B ) 3( 2 A _ 1 45 : 20 2 n A _ x) (87F 150 A6 4) D3. A fiveyear deferred whole life policy pays $10,000 at the moment of death for a person aged 30. Assume a constant force of mortality.05 and a force of interest.10. What is the standard deviation of the present value of the benefit payment? You may use: e e e e A. < $1,820 B. $1,820 but < $1,840 C. $1,840 but < $1,860 D. $1,860 but < $1,880 E. $1,880 ( ) D4. A twentyyear endowment policy is purchased by a man who just turned 30 years old. The policy will pay $10,000 at the moment of death, if he dies within 20 years, or $20,000 if he survives for twenty years. The force of mortality is.01 until age 40 and at age 40 jumps to.02. The force of interest is.10. What is the actuarial present value at policy issue of the benefit payment? A. < $3,100 B. $3,100 but < $3,200 C. $3,200 but < $3,300 D. $3,300 but < $3,400 E. $3,400 ( )
6 314 Insurance Solutions are based on Cunningham, pp , and the pages from Bowers listed below. D1. 1. T, p. 104 For deferred insurance, there is no payout during the deferral period so F Z (0) > F, p. 104 The mode is 0 since this is the probability mass for the deferral period. 3. F, pp. 78, Z < v 30 over two intervals: when t is between 0 and 5, the deferral period, and when t is between 30 and 60. Since probability is uniform under de Moivre's law, their combined probability equals (5 + 30)/60 >.5. Answer: E D2. a. When 0 T < n, Z A 2v T and Z B v T. When T n, Z A v T and Z B 2v T. b. E[Z A ] 2A _ 1 _ x:n + n A _ x c. E[(Z A ) 2 ] 4( 2 A _ 1 _ n:x ) + 2 n A _ x E[(Z B ) 2 ] 2 A _ 1 _ n:x + 4( 2 n A _ x) d. Since (E[Z A ]) 2 (E[Z B ]) 2, we get: Var(Z A ) Var(Z B ) E[(Z A ) 2 ] E[(Z B ) 2 ] 4( 2 A _ 1 _ n:x ) + 2 n A _ x 2 A _ 1 _ n:x 4( 2 n A _ x) D3. 5 A _ 30 e(5)( + Var(Z A ) Var(Z B ) 3( 2 A _ 1 _ n:x ) 3( 2 n A _ x), pp , A_ 30 e(5)( e(5)( ) e(5)( ) e e (10,000) 2 Var( 5 A _ 30) (10,000) 2 [ 2 5 A_ 30 ( 5 A _ 30) 2 ] [(10,000) 2 ][ (.15746) 2 ] (10,000) 2 Var( 5 A _ 30) 3,250,635 Aggregate SD 1,803, p Answer: A D4. The present value has three components: a tenyear term component, a tenyear term component, deferred ten years, and a pure endowment: A _ 1 (1 e ) 30:10 (.01)(1 e(10)(.01+.1) ) A_ 1 (e ' 1 e (10)( ' ) 40:10 10 A_ 1 40:10 (.33287)(1/6)( ) A 30: A 30: (1/11)( ) (e(10)(.01+.1) )(.02)(1 e (10)(.02+.1) ) (e (10)( )(e (10)( '+ ) 2(e (10)(.01+.1) )(e (10)(.02+1) ) (2)(.33287)(.30119) APV [10,000][A _ 1 30: A _ :10 + 2A30: ] APV [10,000] [ ] 2,999, pp Answer: A 20
7 Insurance 315 D5. n A x n+1 A x vq x+n n E x (89F MC) D6. You are given: i) X is the present value random variable for the 25year term insurance of 7 on (35). ii) Y is the present value random variable for the 25year deferred, 10year term insurance of 4 on the same life. iii) E[X] 2.80 and E[Y].12 iv) Var(X) 5.76 and Var(Y).10 Calculate Var(X + Y). A B C D E (90S ) D7. A life aged x is subject to a constant force of mortality, (x).06, and a constant force of interest ( ). A whole life insurance with a death benefit of $20 payable at the moment of death is purchased. The actuarial present value is $12. Determine the actuarial present value if a tenyear deferred whole life insurance with a $20 death benefit was purchase instead. A. < $5 B. $5 but < $6 C. $6 but < $7 D. $7 but < $8 E. $8 (94F 4A 19 2) D8. For a life aged 35, you are given a force of interest,.10, and a force of mortality,.06. This life purchases a tenyear deferred whole life insurance with a benefit of one payable at the moment of death. Z is the present value at policy issue of the benefit for this insurance. Determine the 90th percentile of Z. A. <.30 B..30 but <.40 C..40 but <.50 D..50 but <.60 E..60 (95F 4A 14 2) D9. An endowment insurance has the following provisions: i) ii) A benefit of $0 if the insured dies within five years of policy issue. A benefit of $1 if the insured survives five years but dies within the subsequent seven years. iii) A benefit of $2 at the end of twelve years if the insured survives at least twelve years after policy issue. The death benefit is payable at the moment of death. You also are given the following values with t equal to the number of years from policy issue: t (t) t 0 t t > Determine the actuarial present value for this insurance. A. <.25 B..25 but <.35 C..35 but <.45 D..45 but <.55 E..55 (95F 4A 17 2)
8 316 Insurance D5. T, pp. 101, 118 The expression on the lefthand side of the equation provides term coverage for age (x + n) discounted n years. The term coverage equals vq x+n and the discount factor is n E x, which together comprise the righthand side. D6. Since X and Y are mutually exclusive, E[XY] 0. E[X 2 ] Var(X) + (E[X]) (2.8) E[Y 2 ] Var(Y) + (E[Y]) (.12) Var(X + Y) E[(X + Y) 2 ] (E[X + Y]) 2 E[X 2 ] + 2 E[XY] + E[Y 2 ] (E[X] + E[Y]) 2 Var(X + Y) (2)(0) ( ) , p. 96. Answer: B D7. (20 20A_ x) 20A _ x (20 12)(.06) A _ x (20)(.06)e(10)( ) Answer: A 4.41, pp. 99, 103. D8. 1) Calculate the probability Z equals 0: 10 P(Z 0) P(T 10) e .06t.06 dt 1 e ) Calculate the probability Z is greater than zero but less than the 90th percentile: P(0 < Z.9 ) ) Calculate the 90th percentile, using the same procedure as in A11. log.9 log log.9 / log (.44881).10/ , pp , Answer: A D9. The present value has three components: a threeyear term component deferred five years, a fouryear term component deferred eight years, and a pure endowment: 5 3A _ x v 5 5p x A _ 1 _ x:3 e (5)( + ) ( )(1 e(3)( + ) ) 5 3A _ x (.47237)(1/3)( ) A _ x v 8 8p x A _ 1 _ x:4 e (8)( + ) '(1 e(4)( '+ ') ) ' + ' e (5)( ) (.05)(1 e(3)( ) ) e (8)( ).10(1 e(4)( ) ) A _ x (.30119)(1/2)( ) A 2v 12 x :12 12px 2e (8)( + ) e (4)( '+ ') 2e (8)( ) e (4)( ) 1 2A (2)(.30119)(.44933) x :12 APV 5 3 A _ x A _ x + Answer: C 1 2A , pp , x :12
9 Insurance 317 D10. For a special whole life insurance on (x), you are given: i) (x + t), t 0 ii) t, t 0 iii) The death benefit, payable at the moment of death, is 1 for the first ten years and.5 thereafter. iv) The single benefit premium is v) Z is the present value random variable at issue of the death benefit. Calculate Var (Z). A. <.07 B..07 but.08 C..08 but <.09 D..09 but <.10 E..10 (96F ) D11. The benefit payable under an myear deferred whole life policy, with benefit payable at the moment of death, is twice that of a similar nondeferred whole life insurance. The actuarial present values for these insurances are equal. You may assume constant forces of mortality and interest,.08 and.06. Determine m. A. < 2 B. 2 but < 4 C. 4 but < 6 D. 6 but < 8 E. 8 (97F 4A 10 2) D12. For a special whole life insurance on (t), you are given: i) Benefits are payable at the moment of death. ii) b t 200 for 0 t < 65 iii) b t 100 for t 65 iv) 0 (t).03 for t 0 v) t.01 for 0 t < 65 vi) t.02 for t 65 Calculate the actuarial present value at issue of this insurance. A. 140 B. 141 C. 142 D. 143 E. 144 (98S ) D13. A special insurance program is designed to pay a benefit in the event a product fails. You are given: i) Benefits are payable at the moment of failure. ii) b t 300 and.02 for 0 t < 25 iii) b t 100 and.03 for t 25 iv) (t).04 for t 0 Calculate the actuarial present value of this special insurance. A. 165 B. 168 C. 171 D. 210 E. 213 (Sample 3 11) D14. For a tenyear deferred whole life insurance of 1 payable at the moment of death on a life aged 35, you are given: i) The force of interest is.10. ii) iii) The force of mortality is.06. Z is the present value random variable for this insurance. Determine the 90th percentile of Z. A B C D E (Sample 3 44)
10 318 Insurance D E[Z] A _ 1 _ x:n + (.5)( n A _ x) (1 e10( + ) ).3324 (1 e10( + ) ) E[Z 2 ] (1 e10( +2 ) ) (e10( + ) ) 2() + (e 10( + ) ) 2() 1/2 e 20 / (e10( +2 ) ) (2) 2 1/3 e ( + 2 ) (10)(.06) / Var(Z) E[Z] (E[Z]) (.3324) , pp. 99, 103. Answer: C D11. 2 (e m( + ) ) 2e m( +.06) 1 m log , pp. 99, 103. Answer: C D12. A _ 1 ( )(1 e (65)( + ) ) 0:65 65 A _ 0 e(65)( + ' APV 200A Answer: D 1 0:25 D13. A _ 1 ( )(1 e (25)( + ) ) 0:25 25 A _ 0 e(5)( + ' APV 300A Answer: B 1 (.03)(1 e(65)( ) ) e(65)( ) e (3)(1 e2.6 ) A _ 0 (200)(.69429) + (100)( ) 143, pp , :25 (.04)(1 e(25)( ) ) e(25)( ) e (2)(1 e1.5 ) A _ 0 (300)(.51791) + (100)(.12750) 168, pp , D14. 1) Calculate the probability Z equals 0: 10 P(Z 0) P(T 10) 0 e .06t.06 dt 1 e ) Calculate the probability Z is greater than zero but less than the 90th percentile: P(0 < Z.9 ) ) Calculate the 90th percentile, using the same procedure as in A11. log.9 log log.9 / log (.44881).10/ , pp , Answer: C
11 Insurance 319 D15. An investment fund is established to provide benefits on 400 independent lives age x. i) On January 1, 2001, each life is issued a 10year deferred whole life insurance of 1,000, payable at the moment of death. ii) Each life is subject to a constant force of mortality of.05. iii) The force of interest is.07. Calculate the amount needed in the investment fund on January 1, 2001, so that the probability, as determined by the normal approximation, is.95 that the fund will be sufficient to provide these benefits. A. 55,300 B. 56,400 C. 58,500 D. 59,300 E. 60,100 (00S 3 13) D16. Each of 100 independent lives purchases a single premium fiveyear deferred whole life insurance of 10 payable at the moment of death. You are given: i).04 ii).06 iii) F is the aggregate amount the insurer receives from the 100 lives. Using the normal approximation, calculate F such that the probability the insurer has sufficient funds to pay all claims is.95. A. 280 B. 390 C. 500 D. 610 E. 720 (01F 3 8) D17. Given the following, Calculate 20 A _ x. i) i 5% ii) The force of mortality is constant. iii) e x 16.0 A. <.050 B..050 but <.075 C..075 but <.100 D..100 but <.125 E..125 (03F 3C 7 2) D18. For a whole life insurance of 1,000 on (x) with benefits payable at the moment of death:.04, 0 < t 10 i) t.05, 10 < t.06, 0 < t 10 ii) (x + t).07, 10 < t Calculate the single benefit premium for this insurance. A. 379 B. 411 C. 444 D. 519 E. 594 (03F 3S 2) (Sample M 2) D19. For a fiveyear deferred whole life insurance of 1, payable at the moment of death of (x), you are given: i) Z is the present value random variable of this insurance. ii).10 iii).04 Calculate Var(Z). A. <.035 B..035 but <.045 C..045 but <.055 D..055 but <.065 E..065 (04F 3C 2 2)
12 320 Insurance D A _ x e(10)( +.05 e(10)( ) e E[S] (400)(1,000) 10 A _ x (400)(1,000)(.12550) 50, A_ x e(10)( e(10)( ) e Var(Z) (400)(1,000) 2 Var( 10 A _ x) (400)(1,000) 2 [ 2 10 A_ x ( 10 A _ x) 2 ] Var(Z) [400][(1,000) 2 ][ (.12550) 2 ] (1,000) 2 (9.4439) SD(Z) 3,073 APV E[Z] SD(Z) 50,200 + (1.645)(3,073) 55,255, pp. 99, 103. Answer: A D16. 5 A _ x e(5)( +.04 e(5)( ) e E[Z] (100)(10) 5 A _ x (100)(10)(.24261) A_ x e(5)( e(5)( ) e Var(Z) (100)(10) 2 Var( 5 A _ x) (100)(10) 2 [ 2 5 A_ x ( 5 A _ x) 2 ] Var(Z) [100][(10) 2 ][ (.24261) 2 ] (100) 2 (.05347) SD(Z) F E[Z] SD(Z) (1.645)(23.12) , pp. 99, 103. Answer: A D17. See exercise log / e x 1/ A _ x e(20)( + pp. 87, 99, 103 Answer: B.0625e(20)( ) e , D18. A _ 1 x:10 ( ) )(1 e10( + ) (.06)(1 e(10)( ) ) A _ x 'e(10)( +.07e(10)( ) ' + ' e APV (1,000)( ) , pp. 99, 103. (.6)(1 e 1 ) Answer: E D19. 5 A _ x e(5)( A_ x e(5)( e(5)( ) e(5)( ) (2/7)e e Var(Z) 2 5 A_ x ( 5 A _ x) (.14188) , p. 99, 103. Answer: A
13 Insurance 321 D20. For a fiveyear deferred whole life insurance of one on (x), you are given: i).06 ii).04 iii) The benefit is paid at the moment of death. iv) Z is the present value random variable of the insurance benefit. Calculate Var(Z). A. <.05 B..05 but <.06 C..06 but <.07 D..07 but <.08 E..08 (06F ) D21. An appliance store sells microwave ovens with a threeyear warranty against failure. At the time of purchase, the consumer may buy a twoyear extended warranty that would pay half of the original purchase price at the moment of failure. You are given: i) The extended warranty period begins exactly three years after the time of purchase, but only if the oven has not failed by then. ii) Any failure is considered permanent. iii) 4% iv) Failure of the ovens follows the mortality table below, with uniform distribution of failure within each year: Age (x) q x Calculate the actuarial present value of the extended warranty as a percent of the purchase price. A. < 3.8% B. 3.8% but < 4.1% C. 4.1% but < 4.4% D. 4.4% but < 4.7% E. 4.7% (06F ) D22. For a whole life insurance of 1 on (x) with benefits payable at the moment of death, you are given:.02, t < 12 t {.03, t 12 x (t) {.04, t < 5.05, t 5 Calculate the actuarial present value of this insurance. A..59 B..61 C..64 D..66 E..68 (06F M 12)
14 322 Insurance D20. 5 A _ x e5( +.04e(5)( ) A_ x e5( e[5][.04+(2)(.06)].04 + (2)(.06) Var(Z) 2 5 A_ x ( 5 A _ x) (.24261) , pp. 99, 103. Answer: B D21. Approximate the answer by assuming that failures occur at time t 3.5 and t A _ x (.5)(1 q 0 )(1 q 1 )(1 q 2 )e 3.5 (q 3 + e  q 4 ) A _ x (.5)(1.008)(1.015)(1.026)e (.04)(3.5) ( e ) A _ x (.5)(.95171)(.86936)(.10253).04242, pp. 74, 103, 109. Answer: C D22. A _ x A _ 1 _ A _ x + 12 A _ x x:5 A _ x ( ) )(1 e5( + ) + (e )( 5( + ) ' ) ' + )(1 e7( '+ ) + (e 5( + ) )(e )( 7( '+ ) ' ) ' + ' A _ x ( )(1 e ) 5( ) + (e )( 5( +.02) )(1 e ) 7( ) + (e 5( ) )(e )( 7( ) ) A _ x (2/3)(.25918) + (.74081)(5/7)(.38737) + (.74081)(.61263)(5/8) A _ x , pp. 99, 103. Answer: D
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
More informationInsurance Benefits. Lecture: Weeks 68. Lecture: Weeks 68 (STT 455) Insurance Benefits Fall 2014  Valdez 1 / 36
Insurance Benefits Lecture: Weeks 68 Lecture: Weeks 68 (STT 455) Insurance Benefits Fall 2014  Valdez 1 / 36 An introduction An introduction Central theme: to quantify the value today of a (random)
More informationManual for SOA Exam MLC.
Chapter 4. Life insurance. Extract from: Arcones Fall 2009 Edition, available at http://www.actexmadriver.com/ (#1, Exam M, Fall 2005) For a special whole life insurance on (x), you are given: (i) Z is
More informationManual for SOA Exam MLC.
Chapter 5. Life annuities Extract from: Arcones Fall 2009 Edition, available at http://www.actexmadriver.com/ 1/60 (#24, Exam M, Fall 2005) For a special increasing whole life annuitydue on (40), you
More informationSOCIETY 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
More informationSolution. 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
More informationManual 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)
More informationFundamentals of Actuarial Mathematics
Fundamentals of Actuarial Mathematics S. David Promislow York University, Toronto, Canada John Wiley & Sons, Ltd Contents Preface Notation index xiii xvii PARTI THE DETERMINISTIC MODEL 1 1 Introduction
More informationNovember 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
More informationChapter 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
More informationTABLE 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
More informationJANUARY 2016 EXAMINATIONS. Life Insurance I
PAPER CODE NO. MATH 273 EXAMINER: Dr. C. BoadoPenas TEL.NO. 44026 DEPARTMENT: Mathematical Sciences JANUARY 2016 EXAMINATIONS Life Insurance I Time allowed: Two and a half hours INSTRUCTIONS TO CANDIDATES:
More informationManual for SOA Exam MLC.
Chapter 4. Life Insurance. Extract from: Arcones Manual for the SOA Exam MLC. Fall 2009 Edition. available at http://www.actexmadriver.com/ 1/14 Level benefit insurance in the continuous case In this chapter,
More informationMay 2012 Course MLC Examination, Problem No. 1 For a 2year 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
More informationAnnuities. Lecture: Weeks 911. Lecture: Weeks 911 (STT 455) Annuities Fall 2014  Valdez 1 / 43
Annuities Lecture: Weeks 911 Lecture: Weeks 911 (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:
More informationSOCIETY 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
More information**BEGINNING OF EXAMINATION**
November 00 Course 3 Society of Actuaries **BEGINNING OF EXAMINATION**. You are given: R = S T µ x 0. 04, 0 < x < 40 0. 05, x > 40 Calculate e o 5: 5. (A) 4.0 (B) 4.4 (C) 4.8 (D) 5. (E) 5.6 Course 3: November
More informationPlease 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 (6:008:00 pm) Room: MSB 411 Total Marks: 120 points Please write your name and student number
More informationSOA EXAM MLC & CAS EXAM 3L STUDY SUPPLEMENT
SOA EXAM MLC & CAS EXAM 3L STUDY SUPPLEMENT by Paul H. Johnson, Jr., PhD. Last Modified: October 2012 A document prepared by the author as study materials for the Midwestern Actuarial Forum s Exam Preparation
More informationManual for SOA Exam MLC.
Chapter 6. Benefit premiums. Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/77 Fully discrete benefit premiums In this section, we will consider the funding of insurance
More informationPremium Calculation. Lecture: Weeks 1214. Lecture: Weeks 1214 (STT 455) Premium Calculation Fall 2014  Valdez 1 / 31
Premium Calculation Lecture: Weeks 1214 Lecture: Weeks 1214 (STT 455) Premium Calculation Fall 2014  Valdez 1 / 31 Preliminaries Preliminaries An insurance policy (life insurance or life annuity) is
More informationFurther 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...............................
More informationHeriotWatt University. BSc in Actuarial Mathematics and Statistics. Life Insurance Mathematics I. Extra Problems: Multiple Choice
HeriotWatt 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.
More informationManual for SOA Exam MLC.
Chapter 6. Benefit premiums. Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/24 Nonlevel premiums and/or benefits. Let b k be the benefit paid by an insurance company
More informationACTS 4301 FORMULA SUMMARY Lesson 1: Probability Review. Name f(x) F (x) E[X] Var(X) Name f(x) E[X] Var(X) p x (1 p) m x mp mp(1 p)
ACTS 431 FORMULA SUMMARY Lesson 1: Probability Review 1. VarX)= E[X 2 ] E[X] 2 2. V arax + by ) = a 2 V arx) + 2abCovX, Y ) + b 2 V ary ) 3. V ar X) = V arx) n 4. E X [X] = E Y [E X [X Y ]] Double expectation
More informationTABLE OF CONTENTS. A. PutCall Parity 1 B. Comparing Options with Respect to Style, Maturity, and Strike 13
TABLE OF CONTENTS 1. McDonald 9: "Parity and Other Option Relationships" A. PutCall Parity 1 B. Comparing Options with Respect to Style, Maturity, and Strike 13 2. McDonald 10: "Binomial Option Pricing:
More informationACTUARIAL 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 HeriotWatt University, Edinburgh CAMBRIDGE
More informationManual for SOA Exam MLC.
Chapter 4. Life Insurance. Extract from: Arcones Manual for the SOA Exam MLC. Fall 2009 Edition. available at http://www.actexmadriver.com/ 1/44 Properties of the APV for continuous insurance The following
More information1. Datsenka Dog Insurance Company has developed the following mortality table for dogs:
1 Datsenka Dog Insurance Company has developed the following mortality table for dogs: Age l Age l 0 2000 5 1200 1 1950 6 1000 2 1850 7 700 3 1600 8 300 4 1400 9 0 Datsenka sells an whole life annuity
More informationPremium Calculation. Lecture: Weeks 1214. Lecture: Weeks 1214 (Math 3630) Annuities Fall 2015  Valdez 1 / 32
Premium Calculation Lecture: Weeks 1214 Lecture: Weeks 1214 (Math 3630) Annuities Fall 2015  Valdez 1 / 32 Preliminaries Preliminaries An insurance policy (life insurance or life annuity) is funded
More informationFundamentals of Actuarial Mathematics. 3rd Edition
Brochure More information from http://www.researchandmarkets.com/reports/2866022/ Fundamentals of Actuarial Mathematics. 3rd Edition Description:  Provides a comprehensive coverage of both the deterministic
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 2 Solutions
Math 70/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 2 Solutions About this problem set: These are problems from Course /P actuarial exams that I have collected over the years,
More informationSome 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
More informationMath 630 Problem Set 2
Math 63 Problem Set 2 1. AN nyear term insurance payable at the moment of death has an actuarial present value (i.e. EPV) of.572. Given µ x+t =.7 and δ =.5, find n. (Answer: 11) 2. Given: Ā 1 x:n =.4275,
More informationSOCIETY OF ACTUARIES EXAM M ACTUARIAL MODELS EXAM M SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM M ACTUARIAL MODELS EXAM M SAMPLE QUESTIONS Copyright 5 by the Society of Actuaries Some of the questions in this study note are taken from past SOA examinations. M95 PRINTED
More information4. Life Insurance. 4.1 Survival Distribution And Life Tables. Introduction. X, Ageatdeath. T (x), timeuntildeath
4. Life Insurance 4.1 Survival Distribution And Life Tables Introduction X, Ageatdeath T (x), timeuntildeath Life Table Engineers use life tables to study the reliability of complex mechanical and
More informationb g is the future lifetime random variable.
**BEGINNING OF EXAMINATION** 1. Given: (i) e o 0 = 5 (ii) l = ω, 0 ω (iii) is the future lifetime random variable. T Calculate Var Tb10g. (A) 65 (B) 93 (C) 133 (D) 178 (E) 333 COURSE/EXAM 3: MAY 0001
More informationO MIA009 (F2F) : GENERAL INSURANCE, LIFE AND
No. of Printed Pages : 11 MIA009 (F2F) kr) ki) M.Sc. ACTUARIAL SCIENCE (MSCAS) N December, 2012 0 O MIA009 (F2F) : GENERAL INSURANCE, LIFE AND HEALTH CONTINGENCIES Time : 3 hours Maximum Marks : 100
More informationINSTRUCTIONS 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
More informationMATH 3630 Actuarial Mathematics I Class Test 2 Wednesday, 17 November 2010 Time Allowed: 1 hour Total Marks: 100 points
MATH 3630 Actuarial Mathematics I Class Test 2 Wednesday, 17 November 2010 Time Allowed: 1 hour Total Marks: 100 points Please write your name and student number at the spaces provided: Name: Student ID:
More informationManual for SOA Exam MLC.
Chapter 5. Life annuities. Extract from: Arcones Manual for the SOA Exam MLC. Spring 2010 Edition. available at http://www.actexmadriver.com/ 1/114 Whole life annuity A whole life annuity is a series of
More information1 Cashflows, discounting, interest rate models
Assignment 1 BS4a Actuarial Science Oxford MT 2014 1 1 Cashflows, discounting, interest rate models Please hand in your answers to questions 3, 4, 5 and 8 for marking. The rest are for further practice.
More informationSOCIETY OF ACTUARIES EXAM M ACTUARIAL MODELS EXAM M SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM M ACTUARIAL MODELS EXAM M SAMPLE QUESTIONS Copyright 005 by the Society of Actuaries Some of the questions in this study note are taken from past SOA examinations. M0905 PRINTED
More informationManual for SOA Exam MLC.
Chapter 4. Life Insurance. c 29. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam MLC. Fall 29 Edition. available at http://www.actexmadriver.com/ c 29. Miguel A. Arcones.
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 5 Solutions
Math 370/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 5 Solutions About this problem set: These are problems from Course 1/P actuarial exams that I have collected over the
More informationINSTITUTE 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
More informationJoint Exam 1/P Sample Exam 1
Joint Exam 1/P Sample Exam 1 Take this practice exam under strict exam conditions: Set a timer for 3 hours; Do not stop the timer for restroom breaks; Do not look at your notes. If you believe a question
More informationYanyun Zhu. Actuarial Model: Life Insurance & Annuity. Series in Actuarial Science. Volume I. ir* International Press. www.intlpress.
Yanyun Zhu Actuarial Model: Life Insurance & Annuity Series in Actuarial Science Volume I ir* International Press www.intlpress.com Contents Preface v 1 Interest and AnnuityCertain 1 1.1 Introduction
More informationManual for SOA Exam MLC.
Manual for SOA Eam MLC. Chapter 4. Life Insurance. Etract from: Arcones Manual for the SOA Eam MLC. Fall 2009 Edition. available at http://www.actemadriver.com/ Manual for SOA Eam MLC. 1/9 Payments at
More informationINSTITUTE 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
More informationMath 419B Actuarial Mathematics II Winter 2013 Bouillon 101 M. W. F. 11:00 11:50
Math 419B Actuarial Mathematics II Winter 2013 Bouillon 101 M. W. F. 11:00 11:50 1 Instructor: Professor Yvonne Chueh Office: Bouillon 107G (Tel: 9632124) email: chueh@cwu.edu Office hours: MTh 11:50
More informationINSTITUTE 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
More information1. A survey of a group s viewing habits over the last year revealed the following
1. A survey of a group s viewing habits over the last year revealed the following information: (i) 8% watched gymnastics (ii) 9% watched baseball (iii) 19% watched soccer (iv) 14% watched gymnastics and
More informationCOURSE 3 SAMPLE EXAM
COURSE 3 SAMPLE EXAM Although a multiple choice format is not provided for some questions on this sample examination, the initial Course 3 examination will consist entirely of multiple choice type questions.
More informationEXAM 3, FALL 003 Please note: On a onetime basis, the CAS is releasing annotated solutions to Fall 003 Examination 3 as a study aid to candidates. It is anticipated that for future sittings, only the
More informationPremium Calculation  continued
Premium Calculation  continued Lecture: Weeks 12 Lecture: Weeks 12 (STT 456) Premium Calculation Spring 2015  Valdez 1 / 16 Recall some preliminaries Recall some preliminaries An insurance policy (life
More informationPoisson processes (and mixture distributions)
Poisson processes (and mixture distributions) James W. Daniel Austin Actuarial Seminars www.actuarialseminars.com June 26, 2008 c Copyright 2007 by James W. Daniel; reproduction in whole or in part without
More informationEXAMINATION. 6 April 2005 (pm) Subject CT5 Contingencies Core Technical. Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE
Faculty of Actuaries Institute of Actuaries EXAMINATION 6 April 2005 (pm) Subject CT5 Contingencies Core Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and
More informationNovember 2000 Course 3
November Course 3 Society of Actuaries/Casualty Actuarial Society November   GO ON TO NEXT PAGE Questions through 36 are each worth points; questions 37 through 44 are each worth point.. For independent
More information( ) = 1 x. ! 2x = 2. The region where that joint density is positive is indicated with dotted lines in the graph below. y = x
Errata for the ASM Study Manual for Exam P, Eleventh Edition By Dr. Krzysztof M. Ostaszewski, FSA, CERA, FSAS, CFA, MAAA Web site: http://www.krzysio.net Email: krzysio@krzysio.net Posted September 21,
More informationSOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE WRITTENANSWER QUESTIONS AND SOLUTIONS
SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE WRITTENANSWER QUESTIONS AND SOLUTIONS Questions February 12, 2015 In Questions 12, 13, and 19, the wording was changed slightly
More informationThe Actuary s Free Study Guide for. Second Edition G. Stolyarov II,
The Actuary s Free Study Guide for Exam 3L Second Edition G. Stolyarov II, ASA, ACAS, MAAA, CPCU, ARe, ARC, API, AIS, AIE, AIAF First Edition Published in AugustOctober 2008 Second Edition Published in
More informationMath 370, Spring 2008 Prof. A.J. Hildebrand. Practice Test 2
Math 370, Spring 2008 Prof. A.J. Hildebrand Practice Test 2 About this test. This is a practice test made up of a random collection of 15 problems from past Course 1/P actuarial exams. Most of the problems
More informationINSURANCE 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
More informationErrata and updates for ASM Exam C/Exam 4 Manual (Sixteenth Edition) sorted by page
Errata for ASM Exam C/4 Study Manual (Sixteenth Edition) Sorted by Page 1 Errata and updates for ASM Exam C/Exam 4 Manual (Sixteenth Edition) sorted by page Practice exam 1:9, 1:22, 1:29, 9:5, and 10:8
More informationMath 370, Spring 2008 Prof. A.J. Hildebrand. Practice Test 2 Solutions
Math 370, Spring 008 Prof. A.J. Hildebrand Practice Test Solutions About this test. This is a practice test made up of a random collection of 5 problems from past Course /P actuarial exams. Most of the
More informationSTAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400&3400 STAT2400&3400 STAT2400&3400 STAT2400&3400 STAT3400 STAT3400
Exam P Learning Objectives All 23 learning objectives are covered. General Probability STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 1. Set functions including set notation and basic elements
More informationProfit Measures in Life Insurance
Profit Measures in Life Insurance Shelly Matushevski Honors Project Spring 2011 The University of Akron 2 Table of Contents I. Introduction... 3 II. Loss Function... 5 III. Equivalence Principle... 7 IV.
More informationFinance 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
More information**BEGINNING OF EXAMINATION**
Fall 2002 Society of Actuaries **BEGINNING OF EXAMINATION** 1. Given: The survival function s x sbxg = 1, 0 x < 1 x d i { }, where s x = 1 e / 100, 1 x < 45. = s x 0, 4.5 x Calculate µ b4g. (A) 0.45 (B)
More informationPremium 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
More informationMathematics of Life Contingencies. Math 3281 3.00 W Instructor: Edward Furman Homework 1
Mathematics of Life Contingencies. Math 3281 3.00 W Instructor: Edward Furman Homework 1 Unless otherwise indicated, all lives in the following questions are subject to the same law of mortality and their
More informationExam P  Total 23/23  1 
Exam P Learning Objectives Schools will meet 80% of the learning objectives on this examination if they can show they meet 18.4 of 23 learning objectives outlined in this table. Schools may NOT count a
More informationSOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS Copyright 005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study
More informationInstitute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
More informationChapter 2 Premiums and Reserves in Multiple Decrement Model
Chapter 2 Premiums and Reserves in Multiple Decrement Model 2.1 Introduction A guiding principle in the determination of premiums for a variety of life insurance products is: Expected present value of
More informationLIFE INSURANCE AND PENSIONS by Peter Tryfos York University
LIFE INSURANCE AND PENSIONS by Peter Tryfos York University Introduction Life insurance is the business of insuring human life: in return for a premium payable in one sum or installments, an insurance
More informationEDUCATION AND EXAMINATION COMMITTEE SOCIETY OF ACTUARIES RISK AND INSURANCE. Copyright 2005 by the Society of Actuaries
EDUCATION AND EXAMINATION COMMITTEE OF THE SOCIET OF ACTUARIES RISK AND INSURANCE by Judy Feldman Anderson, FSA and Robert L. Brown, FSA Copyright 25 by the Society of Actuaries The Education and Examination
More informationGLOSSARY. A contract that provides for periodic payments to an annuitant for a specified period of time, often until the annuitant s death.
The glossary contains explanations of certain terms and definitions used in this prospectus in connection with the Group and its business. The terms and their meanings may not correspond to standard industry
More informationStochastic Analysis of LongTerm MultipleDecrement Contracts
Stochastic Analysis of LongTerm MultipleDecrement Contracts Matthew Clark, FSA, MAAA, and Chad Runchey, FSA, MAAA Ernst & Young LLP Published in the July 2008 issue of the Actuarial Practice Forum Copyright
More informationMathematics of Life Contingencies MATH 3281
Mathematics of Life Contingencies MATH 3281 Life annuities contracts Edward Furman Department of Mathematics and Statistics York University February 13, 2012 Edward Furman Mathematics of Life Contingencies
More informationMath 370, Spring 2008 Prof. A.J. Hildebrand. Practice Test 1 Solutions
Math 70, Spring 008 Prof. A.J. Hildebrand Practice Test Solutions About this test. This is a practice test made up of a random collection of 5 problems from past Course /P actuarial exams. Most of the
More informationAdvanced Fixed Income Analytics Lecture 1
Advanced Fixed Income Analytics Lecture 1 Backus & Zin/April 1, 1999 Vasicek: The Fixed Income Benchmark 1. Prospectus 2. Models and their uses 3. Spot rates and their properties 4. Fundamental theorem
More informationEffective 5/10/ A Standard Nonforfeiture Law for Life Insurance.
Effective 5/10/2016 31A22408 Standard Nonforfeiture Law for Life Insurance. (1) (a) This section is known as the "Standard Nonforfeiture Law for Life Insurance." (b) This section does not apply to group
More informationApproximation of Aggregate Losses Using Simulation
Journal of Mathematics and Statistics 6 (3): 233239, 2010 ISSN 15493644 2010 Science Publications Approimation of Aggregate Losses Using Simulation Mohamed Amraja Mohamed, Ahmad Mahir Razali and Noriszura
More informationLloyd Spencer Lincoln Re
AN OVERVIEW OF THE PANJER METHOD FOR DERIVING THE AGGREGATE CLAIMS DISTRIBUTION Lloyd Spencer Lincoln Re Harry H. Panjer derives a recursive method for deriving the aggregate distribution of claims in
More informationQuantitative Methods for Finance
Quantitative Methods for Finance Module 1: The Time Value of Money 1 Learning how to interpret interest rates as required rates of return, discount rates, or opportunity costs. 2 Learning how to explain
More information3. The Economics of Insurance
3. The Economics of Insurance Insurance is designed to protect against serious financial reversals that result from random evens intruding on the plan of individuals. Limitations on Insurance Protection
More informationSOCIETY OF ACTUARIES EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS Copyright 015 by the Society of Actuaries Some of the questions in this study note are taken from past examinations. Some of the questions
More informationMultistate transition models with actuarial applications c
Multistate transition models with actuarial applications c by James W. Daniel c Copyright 2004 by James W. Daniel Reprinted by the Casualty Actuarial Society and the Society of Actuaries by permission
More informationAPPENDIX 4  LIFE INSURANCE POLICIES PREMIUMS, RESERVES AND TAX TREATMENT
APPENDIX 4  LIFE INSURANCE POLICIES PREMIUMS, RESERVES AND TAX TREATMENT Topics in this section include: 1.0 Types of Life Insurance 1.1 Term insurance 1.2 Type of protection 1.3 Premium calculation for
More informationTHE 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
More informationSOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS Copyright 007 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study
More informationADDITIONAL STANDARDS FOR GUARANTEED MINIMUM DEATH BENEFITS for Individual Deferred Variable Annuities
ADDITIONAL STANDARDS FOR GUARANTEED MINIMUM DEATH BENEFITS for Scope: These standards apply to guaranteed minimum death benefits (GMDB) that are built into individual deferred variable annuity contracts
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 3 Solutions
Math 37/48, Spring 28 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 3 Solutions About this problem set: These are problems from Course /P actuarial exams that I have collected over the years,
More informationLIFE 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 standalone
More informationThe Impact of the IRS Retirement Option Relative Value
University of Connecticut DigitalCommons@UConn Honors Scholar Theses Honors Scholar Program May 2005 The Impact of the IRS Retirement Option Relative Value Robert Folan University of Connecticut Follow
More informationProperties of Future Lifetime Distributions and Estimation
Properties of Future Lifetime Distributions and Estimation Harmanpreet Singh Kapoor and Kanchan Jain Abstract Distributional properties of continuous future lifetime of an individual aged x have been studied.
More informationWHAT 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
More informationManual for SOA Exam MLC.
Chapter 5 Life annuities Extract from: Arcones Manual for the SOA Exam MLC Fall 2009 Edition available at http://wwwactexmadrivercom/ 1/94 Due n year temporary annuity Definition 1 A due n year term annuity
More information