Boland P.J. Statistical and Probabilistic Methods in Actuarial Science

CRC Press; Taylor & Francis Group, 2007. — 362 p. — (Interdisciplinary Statistics Series). — ISBN13: 978-1-58488-696-9.Statistical and Probabilistic Methods in Actuarial Science covers many of the diverse methods in applied probability and statistics for students aspiring to careers in insurance, actuarial science, and finance. The book builds on students' existing knowledge of probability and statistics by establishing a solid and thorough understanding of these methods. It also emphasizes the wide variety of practical situations in insurance and actuarial science where these techniques may be used.
Although some chapters are linked, several can be studied independently from the others. The first chapter introduces claims reserving via the deterministic chain ladder technique. The next few chapters survey loss distributions, risk models in a fixed period of time, and surplus processes, followed by an examination of credibility theory in which collateral and sample information are brought together to provide reasonable methods of estimation. In the subsequent chapter, experience rating via no claim discount schemes for motor insurance provides an interesting application of Markov chain methods. The final chapters discuss generalized linear models and decision and game theory.
Developed by an author with many years of teaching experience, this text presents an accessible, sound foundation in both the theory and applications of actuarial science. It encourages students to use the statistical software package R to check examples and solve problems.Claims Reserving and Pricing with Run-Off Triangles
Loss Distributions
Risk Theory
Ruin Theory
Credibility Theory
No Claim Discounting in Motor Insurance
Generalized Linear Models
Decision and Game TheoryBasic Probability Distributions
Some Basic Tools in Probability and Statistics
An Introduction to Bayesian Statistics
Answers to Selected Problems