Probability for Risk Management - Hassett 2006.pdf - Risk Management - Krzysztofx

PROBABILITY

F'OR

RISK MANAGtr,Mtr,NT

Matthew J. Hassett, ASA, Ph.D.

and

Donald G. Stewart, Ph.D.

Department of Mathematics and Statistics

Arizona State University

ACTEX Publications, Inc.

Winsted, Connecticut

by ACTEX Publications, Inc.

No portion of this book may be reproduced in

any form or by any means without prior written

permission from the copy'right owner.

Requests for permission should be addressed to

ACTEX Publications, Inc.

P.O. Box 974

Winsted, CT 06098

Manufactured in the United States of America

10987654321

Cover design by Christine Phelps

Library of Congress Cataloging-in-Publication Data

Hassett, Matthew J.

Probability for risk management / by Matthew J. Hassett and Donald

G. Stewart. -- 2nd ed.

p.cm.

Includes bibliographical references and index.

ISBN-13: 978-1-56698-583-3 (pbk. : alk. paper)

ISBN-10: I -56698-548-X (alk. paper)

1. Risk management--Statistical methods, 2. Risk (lnsurance)--

Statistical methods. 3. Probabilities. I. Stewart, Donald, 1933- II. Title.

HD6t.H35 2006

658.15'5--dc22

2006021589

ISBN-l 3 : 97 8-l -56698-583-3

ISBN-10: l -56698-548-X

Preface

to the Second Edition

The major change in this new edition is an increase in the number of

challenging problems. This was requested by our readers. Since the

actuarial examinations are an exceiient source of challenging problems,

we have added 109 sample exam problems to our exercise sections.

(Detailed solutions can be found in the solutions manual). We thank the

Sociefy of Actuaries for permission to use these problems.

We have added three new sections which cover the bivariate normal

distribution, joint moment generating functions and the multinomial

distribution.

The authors would like to thank the second edition review team:

Leonard A. Asimow, ASA, Ph.D. Robert Morris University, and

Krupa S. Viswanathan, ASA, Ph.D., Temple University.

Finally we would like to thank Gail Hall for her editorial work on the

text and Marilyn Baleshiski for putting the book together.

Matt Hassett

Don Stewart

Tempe, Arizona

June,2006

Preface

This text provides a first course in probability for students with a basic

calculus background. It has been designed for students who are mostly

interested in the applications of probability to risk management in vital

modern areas such as insurance, finance, economics, and health sciences.

The text has many features which are tailored for those students.

Integration of applications and theory. Much of modem probability

theory was developed for the analysis of important risk management

problems. The student will see here that each concept or technique

applies not only to the standard card or dice problems, but also to the

analysis of insurance premiums, unemployment durations, and lives of

mortgages. Applications are not separated as if they were an afterthought

to the theory. The concept of pure premium for an insurance is

introduced in a section on expected value because the pure premium is an

expected value.

Relevant applications. Applications will be taken from texts, published

studies, and practical experience in actuarial science, finance, and

economics.

Development of key ideas through well-chosen examples. The text is

not abstract, axiomatic or proof-oriented. Rather, it shows the student

how to use probability theory to solve practical problems. The student

will be inhoduced to Bayes' Theorem with practical examples using

trees and then shown the relevant formula. Expected values of

distributions such as the gamma will be presented as useful facts, with

proof left as an honors exercise. The student will focus on applying

Bayes' Theorem to disease testing or using the gamma distribution to

model claim severity.

Emphasis on intuitive understanding. Lack of formal proofs does not

correspond to a lack of basic understanding. A well-chosen tree example

shows most students what Bayes' Theorem is really doing. A simple

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