# Installment Joint Life Insurance Actuarial Models with the Stochastic Interest Rate

Save this PDF as:
Size: px
Start display at page:

Download "Installment Joint Life Insurance Actuarial Models with the Stochastic Interest Rate"

## Transcription

2 T xy is the joit life of the couple, x is the husbad who is at the age of x, y is the wife who is at the age of y. The ti-iflatio Model The policy-holder is at the age of x, his future livig time is T. Let the policy-holder buys years term life isurace, the holder pays the fee m times per year for the same iterval, the holder pays the equal fee at the begiig of each iterval. The paymet deadlie is years, if the holder dies durig the years, he stops payig. Let Ct be the paymet fuctio, the stochastic variable of the paymet s preset value is C T Z T e T T () Cosumer price idex (CPI) is the macroecoomic idicator of the geeral household cosumptio of goods ad services. I order to deal with iflatio, isurace compaies lauch a variable life isurace; the isured amout will chage with the time. Table. The real purchasig power of two id s life isurace fee (Uit: Te Thousad yua) C t C t e The loss of The loss of.6t C t C t..6. I Tab., C t is the equal isurace ad C t e.6t is the variable isurace. s ca be see from Tab., the loger the equal life isurace duratio is, the more moey the policy-holder loses. While the variable life isurace has a better ability to resist the ris, it ca effectively resist the.6t damage of iflatio. From Tab., let Ct e be the paymet of variable isurace i this paper. The Force of Iterest ccumulatio Fuctio I the paper, we use the Wieer process ad Poisso process to simulate the fluctuatio of the iterest rate. Let the force of iterest accumulatio fuctio be t, t is give by t tw t Pt t () where Wt follows stadardized Wieer process, Pt follows Poisso process ad the parameter is, W t ad Pt are mutual idepedet., ad are all real umber, which are equal or greater tha. Lemmas Lemma. ssumig that W t follows stadardized Wieer process, Pt follows Poisso process ad the parameter is, W t ad P t are idepedet., ad are real umber, which are equal or greater tha. If t tw t Pt t, the 3

3 b t b E e exp bt b t te Fb, t. [5] (3) Lemma. Let i ad j satisfy i j, the exp,,.[5] (4) E b i b j F b j i F b i Istallmet Joit Life Isurace ctuarial Models with the Stochastic Iterest Rate Net Sigle Premium Let xy : be joit life isurace et sigle premium, xy : is give by t Txy E Z : t E E E C t e E E W Z t f t dt xy W P T P t E E W P C t e t pxt py x t y t dt CtEe p p dt t x t y t x t y t (5) ccordig to Lemma ad Lemma, we ca get exp t x t y xt yt C xy: t t t t e p p dt (6) ccordig to Formula (3), xy : is expressio as xy: C t F t p p dt, t x t y xt yt (7) Survivorship uity ual Survivorship uity. x ad y are i the state of joit life, they pay the fee at the begiig of the year, the amout is a uit of discrete joit life auity. We mar the amout as xy :, xy : is give by xy: px pye e exp e px py px pyf, (8) Mothly Survivorship uity. x ad y are i the state of joit life, they pay the fee at the begiig of the moth, the amout is a uit of discrete joit life auity. We mar the amout as & is expressio as &, a xy : a xy : xy: p p E e x y p exp x py e 33

4 p p F, x y (9) Net Level Premium Net Level Premium of ual Paymet of Life Isurace. x ad y are i the state of joit life. Let P xy : P xy be the aual et level premium, : is give by t t t e p p t x t y xtyt exp : C t xy dt P xy : exp xy : p p t t te x y C t F t p p dt t x t y, xtyt p p F, x y () Net Level Premium of Mothly Paymet of Life Isurace. x ad y are i the state of joit life, let be the mothly et level premium, is give by P xy :, t t x t y t P xy : xy: C t F t p x p y dt P xy: xy: p p F, x y Reserve of the Isurace Compay Reserve of ual Paymet of Life Isurace. I the state of joit life, let clxy be the future loss of isurace compay at the time c, clxy is give by () J clxy CcJe P xy : xy: J () where J is the future livig time of xy at the time c. Let c V xy be the reserve of the isurace compay at the time c, we ca get V E( L ) c xy c xy c c ( ct) ( ) ( ) ( ) ( xy: CctEe ) tpxc tpyc xctyctdtp E IJ Ke c, t xc t yyc xct yc+ t CtF t p p dt, t x t y y xt y+ t C t F t p p dt c t xc t yc px pyf, p p F, (3) 34

5 Reserve of Mothly Paymet of Life Isurace. I the state of joit life, let be the future loss of isurace compay at the time c, is give by clxy clxy J clxy C c J e P xy: xy J : (4) Let V be the reserve of the isurace compay at the time c, we ca get c xy c c xy, t xc t yc xctyct V C c t F t p p dt, c t x t y x t yt px pyf CtF t p p dt pxc pyc F,, (5) Coclusios This paper studies the istallmet joit life isurace actuarial models with the stochastic iterest rate. Firstly, accordig to the aalysis of Chia's cosumer price idex data, the paper poits out the impact of price icreases to policy-holders, the put the cosumer price idex ito the life isurace actuarial models ad costruct life isurace actuarial models. The model has the capacity of ati-iflatioary. Secodly, the paper builds joit life isurace actuarial models. It discusses the aual ad mothly paymet with the stochastic iterest rate. Thirdly, this paper preset the model about the isurace compay reserves. The model we proposed provides a method to determie the loss of life isurace compay i future. cowledgemet This research was fiacially supported by the Graduate Traiig Fud of Harbi Egieerig Uiversity. Refereces [] Pajer H H, Bellhouse D R. Stochastic modelig of iterest rate with applicatios to life cotigecies [J]. Joural of Ris ad Isurace, pp. 9-, 98. [] Beema J, Fuellig C P. Iterest ad mortality radomess i some auities [J]. Isurace: Mathematics ad Ecoomics, 9(), 85-96P, 99. [3] Qigrog Jiag. Whole Life Isurace with the Stochastic Iterest Rate [J]. Joural of Hagzhou Uiversity, 4(), pp.95-99, 997. [4] Wejiog He, Qigrog Jiag. Icreasig Life Isurace with the Stochastic Iterest Rate [J]. Joural of pplied Mathematics, 3(), pp.45-5, 998. [5] Jig Wei, Yogmao Wag. The Reserve of Cotiuous Icreasig Life Isurace with the Stochastic Iterest Rate [J]. Joural of Yasha Uiversity, 3(), pp.-4, 6. 35

### Subject CT5 Contingencies Core Technical Syllabus

Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value

### Institute of Actuaries of India Subject CT1 Financial Mathematics

Istitute of Actuaries of Idia Subject CT1 Fiacial Mathematics For 2014 Examiatios Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig i

### Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

### 5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso

### You are given that mortality follows the Illustrative Life Table with i 0.06 and that deaths are uniformly distributed between integral ages.

1. A 2 year edowmet isurace of 1 o (6) has level aual beefit premiums payable at the begiig of each year for 1 years. The death beefit is payable at the momet of death. You are give that mortality follows

### FI A CIAL MATHEMATICS

CHAPTER 7 FI A CIAL MATHEMATICS Page Cotets 7.1 Compoud Value 117 7.2 Compoud Value of a Auity 118 7.3 Sikig Fuds 119 7.4 Preset Value 122 7.5 Preset Value of a Auity 122 7.6 Term Loas ad Amortizatio 123

### Chapter 7. V and 10. V (the modified premium reserve using the Full Preliminary Term. V (the modified premium reserves using the Full Preliminary

Chapter 7 1. You are give that Mortality follows the Illustrative Life Table with i 6%. Assume that mortality is uiformly distributed betwee itegral ages. Calculate: a. Calculate 10 V for a whole life

### Annuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.

Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio - Israel Istitute of Techology, 3000, Haifa, Israel I memory

### TO: Users of the ACTEX Review Seminar on DVD for SOA Exam MLC

TO: Users of the ACTEX Review Semiar o DVD for SOA Eam MLC FROM: Richard L. (Dick) Lodo, FSA Dear Studets, Thak you for purchasig the DVD recordig of the ACTEX Review Semiar for SOA Eam M, Life Cotigecies

### TO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2

TO: Users of the ACTEX Review Semiar o DVD for SOA Exam FM/CAS Exam FROM: Richard L. (Dick) Lodo, FSA Dear Studets, Thak you for purchasig the DVD recordig of the ACTEX Review Semiar for SOA Exam FM (CAS

### .04. This means \$1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

### Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

No-life isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy

### PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM

PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical ad Mathematical Scieces 2015, 1, p. 15 19 M a t h e m a t i c s AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM A. G. GULYAN Chair of Actuarial Mathematics

### CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

### I. Why is there a time value to money (TVM)?

Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios

### 2 Time Value of Money

2 Time Value of Moey BASIC CONCEPTS AND FORMULAE 1. Time Value of Moey It meas moey has time value. A rupee today is more valuable tha a rupee a year hece. We use rate of iterest to express the time value

### Data Analysis and Statistical Behaviors of Stock Market Fluctuations

44 JOURNAL OF COMPUTERS, VOL. 3, NO. 0, OCTOBER 2008 Data Aalysis ad Statistical Behaviors of Stock Market Fluctuatios Ju Wag Departmet of Mathematics, Beijig Jiaotog Uiversity, Beijig 00044, Chia Email:

### Forecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7

Forecastig Chapter 7 Chapter 7 OVERVIEW Forecastig Applicatios Qualitative Aalysis Tred Aalysis ad Projectio Busiess Cycle Expoetial Smoothig Ecoometric Forecastig Judgig Forecast Reliability Choosig the

### Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean

1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.

### FM4 CREDIT AND BORROWING

FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer

### A probabilistic proof of a binomial identity

A probabilistic proof of a biomial idetity Joatho Peterso Abstract We give a elemetary probabilistic proof of a biomial idetity. The proof is obtaied by computig the probability of a certai evet i two

### Evaluating Model for B2C E- commerce Enterprise Development Based on DEA

, pp.180-184 http://dx.doi.org/10.14257/astl.2014.53.39 Evaluatig Model for B2C E- commerce Eterprise Developmet Based o DEA Weli Geg, Jig Ta Computer ad iformatio egieerig Istitute, Harbi Uiversity of

### Modified Line Search Method for Global Optimization

Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

### Learning objectives. Duc K. Nguyen - Corporate Finance 21/10/2014

1 Lecture 3 Time Value of Moey ad Project Valuatio The timelie Three rules of time travels NPV of a stream of cash flows Perpetuities, auities ad other special cases Learig objectives 2 Uderstad the time-value

### Indexed Survivor Universal Life. Agent product guide 15887 7/10

Idexed Survivor Uiversal Life Aget product guide 15887 7/10 Idexed Survivor Uiversal Life is a flexible premium survivor uiversal life isurace policy with a idex-liked iterest creditig feature. Buildig

### Question 2: How is a loan amortized?

Questio 2: How is a loa amortized? Decreasig auities may be used i auto or home loas. I these types of loas, some amout of moey is borrowed. Fixed paymets are made to pay off the loa as well as ay accrued

### Experience Studies on Determining Life Premium Insurance Ratings: Practical Approaches

Eurasia Joural of Busiess ad Ecoomics 2008, 1 (1), 61-82. Eperiece Studies o etermiig Life Premium Isurace Ratigs: Practical Approaches Mirela CRISTEA* Narcis Eduard MITU** Abstract The focus of this article

### Actuarial Models for Valuation of Critical Illness Insurance Products

INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Volume 9, 015 Actuarial Models for Valuatio of Critical Illess Isurace Products P. Jidrová, V. Pacáková Abstract Critical illess

### Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond

What is a bod? Bod Valuatio I Bod is a I.O.U. Bod is a borrowig agreemet Bod issuers borrow moey from bod holders Bod is a fixed-icome security that typically pays periodic coupo paymets, ad a pricipal

### Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT

Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee

### ACTUARIAL TECHNIQUES TO ASSESS THE FINANCIAL PERFORMANCE. INSURANCE APPLICATIONS

Aals of the Uiversity of Petroşai, Ecoomics, 2(2), 22, 7-76 7 ACTUARIAL TECHNIQUE TO AE THE FINANCIAL PERFORMANCE. INURANCE APPLICATION MIHAELA BOTEA, MARINEL NEELUŢ, CORINA IOANĂŞ, MIHAELA GRUIECU * ABTRACT:

### Time Value of Money. First some technical stuff. HP10B II users

Time Value of Moey Basis for the course Power of compoud iterest \$3,600 each year ito a 401(k) pla yields \$2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle

### Research Article Sign Data Derivative Recovery

Iteratioal Scholarly Research Network ISRN Applied Mathematics Volume 0, Article ID 63070, 7 pages doi:0.540/0/63070 Research Article Sig Data Derivative Recovery L. M. Housto, G. A. Glass, ad A. D. Dymikov

### France caters to innovative companies and offers the best research tax credit in Europe

1/5 The Frech Govermet has three objectives : > improve Frace s fiscal competitiveess > cosolidate R&D activities > make Frace a attractive coutry for iovatio Tax icetives have become a key elemet of public

### Formulae And Tables ICFAI. The Icfai University Press

Formulae Ad Tables The Icfai Uiversity Press Formulae ad Tables Board of EditorS : Prof. V R K Chary, CFA Mr. S Sarkar, CFA Mr. Prakash Bhattacharya, CFA Ms. V D M V Lakshmi, CFA ISBN : 8-788-6-4 The Uiversity,

### University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution

Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chi-square (χ ) distributio.

### Case Study. Normal and t Distributions. Density Plot. Normal Distributions

Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca

### The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection

The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity

### CHAPTER 7: Central Limit Theorem: CLT for Averages (Means)

CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:

### Present Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value

Cocept 9: Preset Value Is the value of a dollar received today the same as received a year from today? A dollar today is worth more tha a dollar tomorrow because of iflatio, opportuity cost, ad risk Brigig

### Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model

Tradig the radomess - Desigig a optimal tradig strategy uder a drifted radom walk price model Yuao Wu Math 20 Project Paper Professor Zachary Hamaker Abstract: I this paper the author iteds to explore

### Life Insurance: Your Blueprint for Wealth Transfer Planning. Producer Guide to Private Split Dollar Arrangements. Your future. Made easier.

Life Isurace: Your Blueprit for Wealth Trasfer Plaig Producer Guide to Private Split Dollar Arragemets These materials are ot iteded to be used to avoid tax pealties ad were prepared to support the promotio

### PENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place.

PENSION ANNUITY Policy Coditios Documet referece: PPAS1(7) This is a importat documet. Please keep it i a safe place. Pesio Auity Policy Coditios Welcome to LV=, ad thak you for choosig our Pesio Auity.

### *The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.

Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.

### DAME - Microsoft Excel add-in for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2

Itroductio DAME - Microsoft Excel add-i for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio,

### BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets

BENEIT-CST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal - Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts

### Comparing Credit Card Finance Charges

Comparig Credit Card Fiace Charges Comparig Credit Card Fiace Charges Decidig if a particular credit card is right for you ivolves uderstadig what it costs ad what it offers you i retur. To determie how

### THE TIME VALUE OF MONEY

QRMC04 9/17/01 4:43 PM Page 51 CHAPTER FOUR THE TIME VALUE OF MONEY 4.1 INTRODUCTION AND FUTURE VALUE The perspective ad the orgaizatio of this chapter differs from that of chapters 2 ad 3 i that topics

### INVESTMENT PERFORMANCE COUNCIL (IPC)

INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks

### Application and research of fuzzy clustering analysis algorithm under micro-lecture English teaching mode

SHS Web of Cofereces 25, shscof/20162501018 Applicatio ad research of fuzzy clusterig aalysis algorithm uder micro-lecture Eglish teachig mode Yig Shi, Wei Dog, Chuyi Lou & Ya Dig Qihuagdao Istitute of

### Swaps: Constant maturity swaps (CMS) and constant maturity. Treasury (CMT) swaps

Swaps: Costat maturity swaps (CMS) ad costat maturity reasury (CM) swaps A Costat Maturity Swap (CMS) swap is a swap where oe of the legs pays (respectively receives) a swap rate of a fixed maturity, while

### Approximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find

1.8 Approximatig Area uder a curve with rectagles 1.6 To fid the area uder a curve we approximate the area usig rectagles ad the use limits to fid 1.4 the area. Example 1 Suppose we wat to estimate 1.

### How to read A Mutual Fund shareholder report

Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.

### Beta-Binomial Model and Its Generalizations in the Demand Forecasting for Multiple Slow-Moving

Beta-Biomial Model ad Its Geeralizatios i the Demad Forecastig for Multiple Slow-Movig Alexadre Dolgui Idustrial Egieerig ad Computer Sciece, Ecole des Mies de Sait-tiee, Frace Maksim Pashkevich Exploratory

### Simple Annuities Present Value.

Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX-9850GB PLUS to efficietly compute values associated with preset value auities.

### Time Value of Money, NPV and IRR equation solving with the TI-86

Time Value of Moey NPV ad IRR Equatio Solvig with the TI-86 (may work with TI-85) (similar process works with TI-83, TI-83 Plus ad may work with TI-82) Time Value of Moey, NPV ad IRR equatio solvig with

### Overview of some probability distributions.

Lecture Overview of some probability distributios. I this lecture we will review several commo distributios that will be used ofte throughtout the class. Each distributio is usually described by its probability

### Reliability Analysis in HPC clusters

Reliability Aalysis i HPC clusters Narasimha Raju, Gottumukkala, Yuda Liu, Chokchai Box Leagsuksu 1, Raja Nassar, Stephe Scott 2 College of Egieerig & Sciece, Louisiaa ech Uiversity Oak Ridge Natioal Lab

### CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest

CDs Bought at a Bak verses CD s Bought from a Brokerage Floyd Vest CDs bought at a bak. CD stads for Certificate of Deposit with the CD origiatig i a FDIC isured bak so that the CD is isured by the Uited

### A RANDOM PERMUTATION MODEL ARISING IN CHEMISTRY

J. Appl. Prob. 45, 060 070 2008 Prited i Eglad Applied Probability Trust 2008 A RANDOM PERMUTATION MODEL ARISING IN CHEMISTRY MARK BROWN, The City College of New York EROL A. PEKÖZ, Bosto Uiversity SHELDON

### For Educational Purposes Only

PCSYBL-F For Educatioal Purposes ly The materials preseted i this course represet the opiios ad views of the developers ad/or reviewers. Although these materials may have bee reviewed, the views ad opiios

### A Guide to the Pricing Conventions of SFE Interest Rate Products

A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios

### Domain 1: Designing a SQL Server Instance and a Database Solution

Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

### Volatility of rates of return on the example of wheat futures. Sławomir Juszczyk. Rafał Balina

Overcomig the Crisis: Ecoomic ad Fiacial Developmets i Asia ad Europe Edited by Štefa Bojec, Josef C. Brada, ad Masaaki Kuboiwa http://www.hippocampus.si/isbn/978-961-6832-32-8/cotets.pdf Volatility of

### Inference on Proportion. Chapter 8 Tests of Statistical Hypotheses. Sampling Distribution of Sample Proportion. Confidence Interval

Chapter 8 Tests of Statistical Hypotheses 8. Tests about Proportios HT - Iferece o Proportio Parameter: Populatio Proportio p (or π) (Percetage of people has o health isurace) x Statistic: Sample Proportio

### SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

### I apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice.

IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form Please complete usig BLOCK CAPITALS ad retur the completed form

### Choosing a Mortgage FIXED-RATE MORTGAGES. ADJUSTABLE-RATE MORTGAGES (ARMs)

Choosig A Mortgage Like homes, home mortgages come i all shapes ad sizes: short-term, log-term, fixed, adjustable, jumbo, balloo these are all terms that will soo be familiar to you, if they re ot already.

### CHAPTER 4: NET PRESENT VALUE

EMBA 807 Corporate Fiace Dr. Rodey Boehe CHAPTER 4: NET PRESENT VALUE (Assiged probles are, 2, 7, 8,, 6, 23, 25, 28, 29, 3, 33, 36, 4, 42, 46, 50, ad 52) The title of this chapter ay be Net Preset Value,

### For customers Key features of the Guaranteed Pension Annuity

For customers Key features of the Guarateed Pesio Auity The Fiacial Coduct Authority is a fiacial services regulator. It requires us, Aego, to give you this importat iformatio to help you to decide whether

### Chapter 6: Variance, the law of large numbers and the Monte-Carlo method

Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value

### DC College Savings Plan Helping Children Reach a Higher Potential

529 DC College Savigs Pla Helpig Childre Reach a Higher Potetial reach Sposored by Govermet of the District of Columbia Office of the Mayor Office of the Chief Fiacial Officer Office of Fiace ad Treasury

### I apply to subscribe for a Stocks & Shares ISA for the tax year 20 /20 and each subsequent year until further notice.

IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form Please complete usig BLOCK CAPITALS ad retur the completed form

### Investing in Stocks WHAT ARE THE DIFFERENT CLASSIFICATIONS OF STOCKS? WHY INVEST IN STOCKS? CAN YOU LOSE MONEY?

Ivestig i Stocks Ivestig i Stocks Busiesses sell shares of stock to ivestors as a way to raise moey to fiace expasio, pay off debt ad provide operatig capital. Ecoomic coditios: Employmet, iflatio, ivetory

### TIAA-CREF Wealth Management. Personalized, objective financial advice for every stage of life

TIAA-CREF Wealth Maagemet Persoalized, objective fiacial advice for every stage of life A persoalized team approach for a trusted lifelog relatioship No matter who you are, you ca t be a expert i all aspects

### New job at the Japanese company, would like to know about the health insurance. What's the process to apply for the insurance?

Cabiet ねん かせんぶ ねん しゅが かせんぶ じてん しゅうせい 8-4-2 (2008 年 下 線 部 &2009 年 朱 書 き 下 線 部 時 点 修 正 ) Level 3 Chapter Illess Sectio Public health isurace Cotets Health isurace 1 Possible questio ad backgroud. New job

### Analyzing Longitudinal Data from Complex Surveys Using SUDAAN

Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical

### Enhance Your Financial Legacy Variable Annuity Death Benefits from Pacific Life

Ehace Your Fiacial Legacy Variable Auity Death Beefits from Pacific Life 7/15 20172-15B As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three death beefits that

### Output Analysis (2, Chapters 10 &11 Law)

B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should

### Confidence Intervals for One Mean

Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a

### MEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book)

MEI Mathematics i Educatio ad Idustry MEI Structured Mathematics Module Summary Sheets Statistics (Versio B: referece to ew book) Topic : The Poisso Distributio Topic : The Normal Distributio Topic 3:

Iformatio about Bakruptcy Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea What is the? The Isolvecy Service of Irelad () is a idepedet

### Best of security and convenience

Get More with Additioal Cardholders. Importat iformatio. Add a co-applicat or authorized user to your accout ad you ca take advatage of the followig beefits: RBC Royal Bak Visa Customer Service Cosolidate

### The Gompertz Makeham coupling as a Dynamic Life Table. Abraham Zaks. Technion I.I.T. Haifa ISRAEL. Abstract

The Gompertz Makeham couplig as a Dyamic Life Table By Abraham Zaks Techio I.I.T. Haifa ISRAEL Departmet of Mathematics, Techio - Israel Istitute of Techology, 32000, Haifa, Israel Abstract A very famous

### Ekkehart Schlicht: Economic Surplus and Derived Demand

Ekkehart Schlicht: Ecoomic Surplus ad Derived Demad Muich Discussio Paper No. 2006-17 Departmet of Ecoomics Uiversity of Muich Volkswirtschaftliche Fakultät Ludwig-Maximilias-Uiversität Müche Olie at http://epub.ub.ui-mueche.de/940/

### Disability Income Insurance

Disability Icome Isurace Admiistered by The Parters Group ad Member Compay Kerr Cruickshak Member Compay: Negotiated Limited Time Offer INDIVIDUAL DISABILITY COVERAGE PROGRAM HIGHLIGHTS: Discouted, Specialty,

### Log-Logistic Software Reliability Growth Model

Log-Logistic Software Reliability Growth Model Swapa S. Gokhale ad Kishor S. Trivedi 2y Bours College of Egg. CACC, Dept. of ECE Uiversity of Califoria Duke Uiversity Riverside, CA 9252 Durham, NC 2778-29

### Settling Insurance Claims After a Disaster What you need to know about how to file a claim how the claim process works what s covered and what s not

Settlig Isurace Claims After a Disaster What you eed to kow about how to file a claim how the claim process works what s covered ad what s ot First Steps Cotact your aget or compay immediately. Fid out

### CHAPTER 11 Financial mathematics

CHAPTER 11 Fiacial mathematics I this chapter you will: Calculate iterest usig the simple iterest formula ( ) Use the simple iterest formula to calculate the pricipal (P) Use the simple iterest formula

### ODBC. Getting Started With Sage Timberline Office ODBC

ODBC Gettig Started With Sage Timberlie Office ODBC NOTICE This documet ad the Sage Timberlie Office software may be used oly i accordace with the accompayig Sage Timberlie Office Ed User Licese Agreemet.

### Rainbow options. A rainbow is an option on a basket that pays in its most common form, a nonequally

Raibow optios INRODUCION A raibow is a optio o a basket that pays i its most commo form, a oequally weighted average of the assets of the basket accordig to their performace. he umber of assets is called

### Research Article An Approach to Evaluating Computer Network Security with Intuitionistic Trapezoidal Fuzzy Information

Joural of Cotrol Sciece ad Egieerig, Article ID 604920, 4 pages http://dx.doi.org/10.1155/2014/604920 Research Article A Approach to Evaluatig Computer Network Security with Ituitioistic Trapezoidal Fuzzy

### Advanced Methods for Security Constrained Financial Transmission Rights (FTR)

dvaced Methods for Security ostraied Fiacial Trasmissio Rights (FTR) Stephe Elbert, Steve.Elbert@PNN.gov Kara Kalsi, Kurt Glaesema, Mark Rice, Maria Vlachopoulou, Nig Zhou Pacific Northwest Natioal aboratory,

### Department of Computer Science, University of Otago

Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS-2006-09 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly

### Enhance Your Financial Legacy Variable Annuities with Death Benefits from Pacific Life

Ehace Your Fiacial Legacy Variable Auities with Death Beefits from Pacific Life 9/15 20188-15C FOR CALIFORNIA As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three

### Lesson 17 Pearson s Correlation Coefficient

Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

### INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology

Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology