Actuarial Mathematics & Life-Table Statistics

Actuarial Mathematics & Life-Table Statistics -...

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Unformatted text preview: Actuarial Mathematics and Life-Table Statistics Eric V. Slud Mathematics Department University of Maryland, College Park c ° 2001 c ° 2001 Eric V. Slud Statistics Program Mathematics Department University of Maryland College Park, MD 20742 Contents 0.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi 1 Basics of Probability & Interest 1 1.1 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Theory of Interest . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Variable Interest Rates . . . . . . . . . . . . . . . . . . 10 1.2.2 Continuous-time Payment Streams . . . . . . . . . . . 15 1.3 Exercise Set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5 Useful Formulas from Chapter 1 . . . . . . . . . . . . . . . . . 21 2 Interest & Force of Mortality 23 2.1 More on Theory of Interest . . . . . . . . . . . . . . . . . . . . 23 2.1.1 Annuities & Actuarial Notation . . . . . . . . . . . . . 24 2.1.2 Loan Amortization & Mortgage Refinancing . . . . . . 29 2.1.3 Illustration on Mortgage Refinancing . . . . . . . . . . 30 2.1.4 Computational illustration in Splus . . . . . . . . . . . 32 2.1.5 Coupon & Zero-coupon Bonds . . . . . . . . . . . . . . 35 2.2 Force of Mortality & Analytical Models . . . . . . . . . . . . . 37 i ii CONTENTS 2.2.1 Comparison of Forces of Mortality . . . . . . . . . . . . 45 2.3 Exercise Set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.4 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.5 Useful Formulas from Chapter 2 . . . . . . . . . . . . . . . . . 58 3 Probability & Life Tables 61 3.1 Interpreting Force of Mortality . . . . . . . . . . . . . . . . . . 61 3.2 Interpolation Between Integer Ages . . . . . . . . . . . . . . . 62 3.3 Binomial Variables & Law of Large Numbers . . . . . . . . . . . . . . . . . . . . . . 66 3.3.1 Exact Probabilities, Bounds & Approximations . . . . 71 3.4 Simulation of Life Table Data . . . . . . . . . . . . . . . . . . 74 3.4.1 Expectation for Discrete Random Variables . . . . . . 76 3.4.2 Rules for Manipulating Expectations . . . . . . . . . . 78 3.5 Some Special Integrals . . . . . . . . . . . . . . . . . . . . . . 81 3.6 Exercise Set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.7 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.8 Useful Formulas from Chapter 3 . . . . . . . . . . . . . . . . . 93 4 Expected Present Values of Payments 95 4.1 Expected Payment Values . . . . . . . . . . . . . . . . . . . . 96 4.1.1 Types of Insurance & Life Annuity Contracts . . . . . 96 4.1.2 Formal Relations among Net Single Premiums . . . . . 102 4.1.3 Formulas for Net Single Premiums . . . . . . . . . . . 103 4.1.4 Expected Present Values for m = 1 . . . . . . . . . . . 104 4.2 Continuous Contracts & Residual Life . . . . . . . . . . . . . 106 CONTENTS iii 4.2.1 Numerical Calculations of Life Expectancies...
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This note was uploaded on 11/20/2011 for the course STATISTICS ST3241 taught by Professor Manwai's during the Spring '11 term at National University of Singapore.

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Actuarial Mathematics & Life-Table Statistics -...

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