Actuarial Mathematics for Life Contingent Risks How can actuaries best equip themselves for the products and risk structures of the future? In this ground-breaking textbook, three leaders in actuarial science give a modem perspective on life contingencies. The book begins with ac'tuarial models and theory, emphasizing practi cal applications using computational techniques. The authors then develop a more contemporary outlook, introducing multiple state models, emerging cash flows and embedded options. This expanded edition contains more examples and exercises designed to help with exam preparation as well as developing up-to-date expertise. There are brand new sections and chapters on discrete time Markov processes, on models involving joint lives and on Universal Life insurance and participating traditional insurance. Balancing rigour with intuition, and emphasizing applications, this text book is ideal for university courses, for qualified actuaries wishing to renew and update their skills and for individuals preparing for the professional actu arial examinations of the Society of Actuaries or Institute and Faculty of Actu aries. The book covers the entire SOA MLC syllabus and will be especially valuable for students preparing for the new, long answer exam questions. DAVID c. M. DICKSON is Professor of Actuarial Studies in the Department of Economics at the University of Melbourne. He is a Fellow of the Faculty of Actuaries and of the Institute of Actuaries of Australia. He has twice been awarded the H. M. Jackson Prize of the Institute of Actuaries of Australia, most recently for his book Insurance Risk and Ruin (Cambridge University Press, 2005). MARY R. HARDY holds the CIBC Chair in Financial Risk Management at the University of Waterloo, Ontario. She is a Fellow of the UK Institute and Fac ulty of Actuaries and of the Society of Actuaries. She is a past Vice President of the Society of Actuaries. In 2013 she was awarded the Finlaison Medal of the Institute and Faculty of Actuaries for services to the actuarial profession, in research, teaching and governance. HOWARD R. WATERS is Professor in the Department of Actuarial Mathematics and Statistics at Heriot-Watt University, Edinburgh. He is a Fellow of the Insti tute and Faculty of Actuaries, by whom he was awarded the Finlaison Medal for services to the actuarial profession in 2006. INTERNATIONAL SERIES ON ACTUARIAL SCIENCE Editorial Board Christopher Daykin (Independent Consultant and Actuary) Angus Macdonald (Heriot-Watt University) The International Series on Actuarial Science, published by Cambridge University Press in conjunction with the Institute and Faculty of Actuaries, contains textbooks for students taking courses in or related to actuarial science, as well as more advanced works designed for continuing professional develop ment or for describing and synthesizing research. The series is a vehicle for publishing books that reflect changes and developments in the curriculum, that encourage the introduction of courses on actuarial science in universities, and that show how actuarial science can be used in all areas where there is long term financial risk. A complete list of books in the series can be found at www.cambridge.org/statistics. Recent titles include the following: Solutions Manual for Actuarial Mathematics for Life Contingent Risks (2nd Edition) David C.M. Dickson, Mary R. Hardy & Howard R. Waters Actuarial Mathematics for Life Contingent Risks (2nd Edition) David C.M. Dickson, Mary R. Hardy & Howard R. Waters Risk Modelling in General Insurance Roger J. Gray & Susan M. Pitts Financial Enterprise Risk Management Paul Sweeting Regression Modeling with Actuarial and Financial Applications Ed ward W. Frees Nonlife Actuarial Models Yiu-Kuen Tse Generalized Linear Models for Insurance Data Pi et De Jong & Gillian Z. Heller Market-Valuation Methods in Life and Pension Insurance Thomas Moller & Mogens Steffensen ACTUARIAL MATHEMATICS FOR LIFE CONTINGENT RISKS SECOND EDITION DAVID C. M. DICKSON University of Melbourne MARY R. HARDY University of Waterloo, Ontario HOWARD R. WATERS Heriot-Watt University, Edinburgh CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS University Printing House, Cambridge CB2 8BS, United Kingdom Published in the United States of America by Cambridge University Press, New York Cambridge University Press is part of the University of Cambridge. It furthers the University's mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107044074 ©David C. M. Dickson, Mary R. Hardy and Howard R. Waters 2009, 2013 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2009 6th printing 2012 Second edition 2013 Printed in the United States by Sheridan Inc. A catalogue record for this publication is available from the British Library Dickson, D. C. M. (David C. M.), 1959- Actuarial mathematics for life contingent risks I David C M Dickson, Mary R Hardy, Howard R Waters. - 2nd edition. pages cm Includes bibliographical references. ISBN 978-1-107-04407-4 (Hardback) 1. Insurance-Mathematics. 2. Risk (lnsurance)-Mathematics. I. Hardy, Mary, 1958- Il. Waters, H. R. (Howard Richard) III. Title. HG8781.D528 2013 368'.0l-dc23 2013013708 ISBN 978-1-107-04407-4 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To Carolann, Vivien andPhelim