Actuarial Models: The Mathematics of Insurance, Second Edition thoroughly covers the basic models of insurance processes. It also presents the mathematical frameworks and methods used in actuarial modeling. This second edition provides an even smoother, more robust account of the main ideas and models, preparing students to take exams of the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS). New to the Second Edition * Revises all chapters, especially material on the surplus process * Takes into account new results and current trends in teaching actuarial modeling * Presents a new chapter on pension models * Includes new problems from the 2011-2013 CAS examinations Like its best-selling, widely adopted predecessor, this edition is designed for students, actuaries, mathematicians, and researchers interested in insurance processes and economic and social models. The author offers three clearly marked options for using the text. The first option includes the basic material for a one-semester undergraduate course, the second provides a more complete treatment ideal for a two-semester course or self-study, and the third covers more challenging topics suitable for graduate-level readers.
Preliminary Facts from Probability and Interest Probability and Random Variables Expectation Some Basic Distributions Moment Generating Functions Convergence of Random Variables and Distributions Limit Theorems Conditional Expectations. Conditioning Elements of the Theory of Interest Comparison of Random Variables. Preferences of Individuals A General Framework and First Criteria Comparison of R.V.s and Limit Theorems Expected Utility Non-Linear Criteria Optimal Payment from the Standpoint of an Insured An Individual Risk Model for a Short Period The Distribution of an Individual Payment The Aggregate Payment Premiums and Solvency. Approximations for Aggregate Claim Distributions Some General Premium Principles A Collective Risk Model for a Short Period Three Basic Propositions Counting or Frequency Distributions The Distribution of the Aggregate Claim Premiums and Solvency. Normal Approximation Random Processes and Their Applications I A General Framework and Typical Situations Poisson and Other Counting Processes Compound Processes Markov Chains. Cash Flows in the Markov Environment Random Processes and Their Applications II Brownian Motion and Its Generalizations Martingales Global Characteristics of the Surplus Process A General Framework Ruin Models Criteria Connected with Paying Dividends Survival Distributions The Probability Distribution of Lifetime A Multiple Decrement Model Multiple Life Models Life Insurance Models A General Model Some Particular Types of Contracts Varying Benefits Multiple Decrement and Multiple Life Models On the Actuarial Notation Annuity Models Two Approaches to the Evaluation of Annuities Level Annuities. A Connection with Insurance Some Particular Types of Level Annuities More on Varying Payments Annuities with m-thly Payments Multiple Decrement and Multiple Life Models Premiums and Reserves Premium Annuities Reserves Pensions Plans Valuation of Individual Pension Plans Pension Funding. Cost Methods Risk Exchange: Reinsurance and Coinsurance Reinsurance from the Standpoint of a Cedent Risk Exchange and Reciprocity of Companies Reinsurance Market Appendix References Answers to Exercises Index Exercises appear at the end of each chapter.
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