## Life insurance mathematicsThis concise introduction to life contingencies, the theory behind the actuarial work around life insurance and pension funds, is written for the reader who likes applied mathematics. In addition to the model of life contingencies, the theory of compound interest is explained and it is shown how mortality and other rates can be estimated from observations. The probabilistic model is used consistently (and the traditional deterministic model avoided). Emphasis is put on the general ideas, which are illustrated by means of examples and interpretations. Recursive formulae and reasoning are discussed in detail. For this second, expanded edition numerous exercises (with answers and solutions) have been added. |

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### Contents

The Mathematics of Compound Interest | 1 |

The Future Lifetime of a Life Aged x | 15 |

Life Insurance | 23 |

Copyright | |

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### Common terms and phrases

actuarial annual payments annual premium annuity annuity-due approximation assume assumption Ax+1 causes of decrement Chapter ck+1 commutation functions components confidence interval consider constant corresponding death benefit decrement table defined derived distribution with parameters equation equivalence principle estimator evaluated expected present value expected value expense-loaded premium reserve expression force of interest force of mortality fully discrete future lifetime gamma distribution Goal Seek Hence IA)x identity Illustrative Life Table independent initial age insurance policy insured is alive insurer's loss interest rate k+1V last-survivor number of deaths obtain payable premium is denoted present value random probability distribution probability of death pure endowment Px+k qx+k random variable recursion formula reinsurance risk single premium solution Spreadsheet Exercises sum insured survival technical gain Theory Exercises uniform distribution value of future Var(L Var[L whole life insurance