Statistical and Probabilistic Methods in Actuarial Science

Statistical and Probabilistic Methods in Actuarial Science

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Description

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.show more

Product details

  • Electronic book text | 368 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 25 Illustrations, black and white
  • 158488696X
  • 9781584886969

Table of contents

PREFACE INTRODUCTION Claims Reserving and Pricing with Run-Off Triangles The Evolving Nature of Claims and Reserves Chain Ladder Methods The Average Cost per Claim Method The Bornhuetter-Ferguson or Loss Ratio Method An Example in Pricing Products Statistical Modeling and the Separation Technique Problems Loss Distributions Introduction to Loss Distributions Classical Loss Distributions Fitting Loss Distributions Mixture Distributions Loss Distributions and Reinsurance Problems Risk Theory Risk Models for Aggregate Claims Collective Risk Models Individual Risk Models for S Premiums and Reserves for Aggregate Claims Reinsurance for Aggregate Claims Problems Ruin Theory The Probability of Ruin in a Surplus Process Surplus and Aggregate Claims Processes Probability of Ruin and the Adjustment Coefficient Reinsurance and the Probability of Ruin Problems Credibility Theory Introduction to Credibility Estimates Classical Credibility Theory The Bayesian Approach to Credibility Theory Greatest Accuracy Credibility Theory Empirical Bayes Approach to Credibility Theory Problems No Claim Discounting in Motor Insurance Introduction to No Claim Discount Schemes Transition in a No Claim Discount System Propensity to Make a Claim in NCD Schemes Reducing Heterogeneity with NCD Schemes Problems Generalized Linear Models Introduction to Linear and Generalized Linear Models Multiple Linear Regression and the Normal Model The Structure of Generalized Linear Models Model Selection and Deviance Problems Decision and Game Theory Introduction Game Theory Decision making and Risk Utility and Expected Monetary Gain Problems References Appendix A: Basic Probability Distributions Appendix B: Some Basic Tools in Probability and Statistics Moment Generating Functions Convolutions of Random Variables Conditional Probability and Distributions Maximum Likelihood Estimation Appendix C: An Introduction to Bayesian Statistics Bayesian Statistics Appendix D: Answers to Selected 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 Theoryshow more

Review quote

This book is meant to serve as a textbook for students seeking careers in insurance, actuarial science, or finance. ... The author provides a variety of worked examples in each chapter to illustrate the main ideas, with an emphasis on those of more numerical and practical nature. Although good references for further reading are provided, basic knowledge in probability and statistics is required. This book will also serve as a nice reference for an insurance analyst.-Technometrics, February 2009, Vol. 51, No. 1 ... There are not many other books that cover actuarial topics based on statistical methods in so complete a way as this one. ... this book is quite adequate as a companion book for anyone in involved with the mathematical concepts of statistics and probability models in actuarial science, and it is essential in a university library where these topics are taught.-Journal of Applied Statistics, 2007 This book is aimed both at students of actuarial science and related subjects and at insurance and actuarial practitioners. ... The treatment is clear throughout, with an ample supply of problems and worked examples. The book would be useful both for teachers of actuarial science and for self-study. -N.H. Bingham, Imperial College, International Statistical Review, 2007 ... The book has grown out of lecture notes and gives an overview on mathematical techniques used in actuarial practice. The main focus of the book is general insurance (property and casualty insurance, nonlife insurance). Besides theory, the book gives many exercises and presents R code.-Mario V. Wuthrich, ETH Zurich, The American Statistician, November 2008 This is a very nice book.-Tonglin Zhang, Mathematical Reviews, 2009ashow more