# Fundamentals of Actuarial Mathematics

John Wiley & Sons, Jan 6, 2011 - Mathematics - 424 pages
This 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

 Contents x THE DETERMINISTIC MODEL 1 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 References 443 Copyright