## Fundamentals of Actuarial MathematicsThis book provides a comprehensive introduction to actuarial mathematics, covering both deterministic and stochastic models of life contingencies, as well as more advanced topics such as risk theory, credibility theory and multi-state models. This new edition includes additional material on credibility theory, continuous time multi-state models, more complex types of contingent insurances, flexible contracts such as universal life, the risk measures VaR and TVaR. Key Features: - Covers much of the syllabus material on the modeling examinations of the Society of Actuaries, Canadian Institute of Actuaries and the Casualty Actuarial Society. (SOA-CIA exams MLC and C, CSA exams 3L and 4.)
- Extensively revised and updated with new material.
- Orders the topics specifically to facilitate learning.
- Provides a streamlined approach to actuarial notation.
- Employs modern computational methods.
- Contains a variety of exercises, both computational and theoretical, together with answers, enabling use for self-study.
An ideal text for students planning for a professional career as actuaries, providing a solid preparation for the modeling examinations of the major North American actuarial associations. Furthermore, this book is highly suitable reference for those wanting a sound introduction to the subject, and for those working in insurance, annuities and pensions. |

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### Contents

The basic deterministic model 7 | |

The life table 37 | |

Life annuities 45 | |

Life insurance 60 | |

Insurance and annuity reserves 76 | |

The stochastic approach to insurance and annuities 205 | |

Simpliﬁcations under level beneﬁt contracts 228 | |

The minimum failure time 238 | |

RISK THEORY 259 | |

Risk Assessment 291 | |

An introduction to stochastic processes 308 | |

Poisson processes 324 | |

Ruin models 332 | |

Fractional durations 101 | |

Continuous payments 115 | |

Select mortality 136 | |

Multiplelife contracts 143 | |

Multipledecrement theory 164 | |

Expenses 182 | |

THE STOCHASTIC MODEL 189 | |

Credibility theory 361 | |

Multistate models 389 | |

Appendix A review of probability theory 406 | |

The normal distribution 412 | |

Probability generating functions 423 | |

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10:0 Printer Name 13:12 Printer Name 9:58 Printer Name accumulated Actuarial Mathematics actuarial notation actuarially equivalent alive amount at risk annuity beneﬁts annuity contracts Assume UDD assumption Australian dollar Ax(b ax(c BASIC DETERMINISTIC MODEL beginning at age beneﬁt payments Bk(c c02 JWST022-Promislow October calculate Canadian dollars cashﬂow vector cell Chapter column compute constant interest rate deﬁned deﬁnition denote discount function endowment insurance equal example exercises expected failure ﬁnancial ﬁnd ﬁrst death ﬁxed force of mortality formula forward prices given guaranteed initial premium INSURANCE AND ANNUITY insurance contract insurance policy interest and survivorship investment joint-life JWST022-Promislow October 13 Level annual premiums mthly n-year occurs paid period policyholder premium payable premium payment premiums are payable present value probability provides purchased pure endowment quantity reader reﬂects repayments reserve Section single premium Solution spreadsheet standard notation stochastic sufﬁcient Suppose symbol yearly zero