## Life insurance mathematicsFrom the reviews: "The highly esteemed 1990 first edition of this book now appears in a much expanded second edition. The difference between the first two English editions is entirely due to the addition of numerous exercises. The result is a truly excellent book, balancing ideally between theory and practice. ....As already hinted at above, this book provides the ideal bridge between the classical (deterministic) life insurance theory and the emerging dynamic models based on stochastic processes and the modern theory of finance. The structure of the bridge is very solid, though at the same time pleasant to walk along. I have no doubt that Gerber's book will become the standard text for many years to come. "Metrika, 44, 1996, 2" |

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### Contents

The Mathematics of Compound Interest | 1 |

The Future Lifetime of a Life Aged x | 15 |

Life Annuities | 35 |

Copyright | |

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### Common terms and phrases

actuarial annual premium annuity annuity-due approximation assume assumption Ax+1 Ax+k calculated cause of decrement Chapter ck+1 commutation functions Compound Poisson Compound Poisson Distribution confidence interval consider corresponding decomposed defined derived distribution with parameters equivalence principle estimator evaluated example expected present value expected value expense-loaded premium reserve expenses expression force of interest force of mortality future lifetime gamma distribution IA)X identity independent initial age insurance policy insured is alive integer interest rate interpretation joint-life status k+1V mathematical method mortality gain multiple number of deaths obtain one-year term insurance perpetuity Poisson distribution premium is denoted probability distribution probability of death probability theory pure endowment Px+k qx+k random variable recursive formula reinsurance result risk premium Section 2.6 single premium stop-loss sum insured technical gain Total Claim Amount uniform distribution value of future variance whole life insurance