Table Of ContentFinancial Mathematics for
Actuaries
Second Edition
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Financial Mathematics for
Actuaries
Second Edition
Wai-Sum Chan The Chinese University of Hong Kong, Hong Kong
Yiu-Kuen Tse Singapore Management University, Singapore
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO
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Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
FINANCIAL MATHEMATICS FOR ACTUARIES
Second Edition
Copyright © 2018 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or
mechanical, including photocopying, recording or any information storage and retrieval system now known or to
be invented, without written permission from the publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center,
Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from
the publisher.
ISBN 978-981-3224-66-7
ISBN 978-981-3224-67-4 (pbk)
Desk Editor: Shreya Gopi
Typeset by Stallion Press
Email: [email protected]
Printed in Singapore
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ToBonnie,NikkiandKevin
fortheircontinuously compounded rateofsupport
Wai-SumChan
ToVicky,Germaine,GeraldandGemma
fortheirunyielding forbearance
Yiu-KuenTse
v
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About the Authors
Wai-SumChan,PhD,FSA,HonFIA,CERA,graduated fromtheChineseUniver-
sityofHongKongwithamajorinAccountingandaminorinStatistics. Hepursued
adoctorate inAppliedStatisticsattheFoxSchoolofBusinessManagement, Tem-
ple University (Philadelphia, USA), receiving his PhD in 1989. He qualified as a
Fellow ofthe Society of Actuaries in1995 and Chartered Enterprise Risk Analyst
in 2008. He was conferred an Honorary Fellow by the Institute and Faculty of
Actuaries in 2014. DrChan held teaching and research posts at the National Uni-
versity ofSingapore, theUniversity ofWaterloo and theUniversity ofHongKong
before his present appointment as Professor of Finance at the Chinese University
ofHongKong. DrChan’s research interests include HealthCareFinancing, Actu-
arialModelingandFinancialEconometrics. Hehashadover100scientificarticles
published inscholarly journals. DrChan has been teaching financial and actuarial
courses since1992.
Yiu-Kuen Tse, PhD, FSA, graduated from the University of Hong Kong,
majoring in Economics and Statistics. He obtained his MSc in Statistics and PhD
in Econometrics from the London School of Economics. Hehas been a Fellow of
the Society of Actuaries since 1993. Dr Tse’s research interests are in Empirical
Finance and Financial Econometrics. He is Professor of Economics at the School
ofEconomics,SingaporeManagementUniversity. Hehaspublishedextensivelyin
scholarly journals andistheauthor ofthebook NonlifeActuarial Models: Theory,
Methods and Evaluation. Dr Tse teaches undergraduate Actuarial Science and is
alsoinvolved inmanyexecutivetraining programs.
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Preface to the Second Edition
A good understanding of the fundamental concepts of financial mathematics is
essential for the evaluation of any financial product and instrument. Mastering
conceptsofpresentandfuturevaluesofstreamsofcashflowsunderdifferentinter-
estrateenvironments iscoreforactuariesandfinancialeconomists. Itiswiththese
perspectives inmindthatwewritethistextbook.
This book covers the body of knowledge required by the Society of Actuaries
(SOA) for its Financial Mathematics (FM) Exam. In this second edition, we
expand the book to include topics introduced by the SOA in the FM Exam from
2017 onwards. In particular, in Chapter 3 we include the coverage of interest rate
swaps. Wealso add a chapter on the determination of the rates of interest of vari-
ous financial securities. Someinstitutional aspects of interest rate policies and the
economicmanagement ofCentralBanksarealsodiscussed inthischapter.
Thisbookalsohasachapteronstochasticinterestratemodels. Studentsstudy-
ing for the Institute and Faculty of Actuaries Exam CT1 will also find this book
suitable forthepreparation oftheexam.
Itisourhopethatstudentsinanundergraduatecourseonfinancialmathematics
foractuarieswillfindthisbookuseful. Thisbookcontainsnumerousexamplesand
exercises, some of which are adapted from previous SOAFM Exams. Webelieve
itisalsousefulforstudents preparing fortheactuarial professional examsthrough
self-study.
Users of this book are assumed to have prior knowledge of high school al-
gebra and college level introductory calculus. An appendix on the preview of
mathematics and statistics is included for the benefits of students who require a
quickrevisionoroccasional reference.
Wecontinue toprovide teaching aidstosupport instructors usingthisbookfor
teaching. Instructors who wish to obtain the instructors’ manual for the solutions
of the exercises and/or the slides for use in lectures may write to the publisher at:
[email protected].
Wai-SumChan,PhDFSACERA Yiu-KuenTse,PhDFSA
DepartmentofFinance SchoolofEconomics
ChineseUniversityofHongKong SingaporeManagementUniversity
