Probability and Stochastic Modeling: The Mathematics of Insurance

Ideal for students preparing for level 300 actuarial exams in the US, Actuarial Models: The Mathematics of Insurance provides a comprehensive exposition of insurance process models and presents mathematical setups and methods used in Actuarial Modeling. Divided into three self-contained and explicitly designated parts of different levels of difficulty, this book examines standard as well as advanced topics such as modern utility theory, martingale technique, models with payments of dividends, reinsurance models, and classification of distributions. It provides practical skills in analysis of insurance processes. This text discusses a number of topics not commonly found in existing Actuarial Mathematics textbooks, including achievements of the modern Risk Evaluation theory, premium principles, accuracy of normal and Poisson approximation, and a reinsurance market model. The main text is preceded by introductory chapters containing basic facts from Probability Theory, Calculus, and the Theory of Interest. The reader will not have to refer to outside sources; everything is under one cover and in the same unified notation and style. The book includes many examples, practice problems, and exercises on numerical calculations using Excel®. It includes preliminary examination material for the Society of Actuaries and the Casualty Actuarial Society (CAS), providing, in particular, real problems from past CAS exams.