Actuarial Mathematics for Life Contingent Risks, 2^nd edition, aims to help students in preparation for MLC exam of Society of Actuaries and the CT5 exam of the Institute and Faculty of Actuaries, UK. It may also be useful for some of the university courses and for individuals preparing for professional actuarial examinations. The authors are qualified actuaries and have experience in actuarial science so as to balance theory with practical applications using computational techniques to provide a modern perspective on life contingencies and help students in preparing for the exams.

The book begins with “Traditional actuarial models and theory”. The authors then introduce multiple state models, emerging cash flows and embedded options. The book has been updated from the 1^st edition to include new material on discrete time Markov processes, on models involving joint lives, and on universal life insurance and participating traditional insurance. The 200 plus exercises provide meaningful practice with both long answer and multiple choice questions. The Solutions Manual provides detailed solutions to the text’s exercises.

The book consists of 16 chapters that cover the following topics:

• ∙ The first seven chapters set the context of the traditional actuarial models, theory of life contingencies, survival models, life insurance products valuation/pricing and policy values. Annuities valuation and analysis is covered separately in chapter 5.

• ∙ From chapter 8 onwards, modern actuarial theory is discussed. The range of topics discussed are:

  • ○ Multiple state models

  • ○ Joint lives

  • ○ Pension mathematics

  • ○ Interest rate models and Monte Carlo simulation

  • ○ Surplus projections and profit testing of life insurance business

  • ○ Guarantees and embedded options – application of options theory

The book is well written and the content is generally quite accessible. It assumes prior knowledge of mathematics of finance, probability and statistical distribution functions. The content focuses on examples of practical actuarial work through use of spreadsheets. Thus, knowledge of basic Excel functions is useful to construct spreadsheet tables for cash flows modelling.

Overall, the book provides good framework in life insurance contingencies so as to cover mortality, longevity, interest rate modelling, pricing and guarantees. The strength of the book lies in the fact that this is 2^nd edition and reflects on the modern actuarial methods that have become popular since last edition was published.

I would recommend the book as a useful supplementary material for actuarial students or anyone interested in understanding mathematics of life insurance business.