Table Of Content

ISBN: 0-936031-10-7 PENSION MATHEMATICS _ _ FOR ACTUARIES Second Edition _ ArihurW . Anderson Digitized by the Internet Archive in 2021 with funding from Kahle/Austin Foundation © https ://archive.org/details/pensionmathemati0000ande Pension Mathematics for Actuaries by Arthur W. Anderson Second Edition ACTEX Publications e Winsted, Connecticut Copyright © 1992 by ACTEX Publications, Inc. All rights reserved No portion of this book may be copied, reproduced, or coded electronically for any purpose whatsoever without written permission from the publisher. 1st printing — February 1985 2nd printing — September 1985 2nd edition — January 1990 2nd edition, 2nd printing — November 1991 2nd edition, 3rd printing — May 1992 Printed in the United States of America Cover Design by MUF Library of Congress Cataloging-in-Publication Data Anderson, Arthur W., 1941 - Pension mathematics for actuaries Includes index. 1. Insurance, Life -- Mathematics. 2. Old age pensions -- Mathematics. I. Title. HG8782.A497 1985 502.22 OL 85-11231 ISBN 0-936031-10-7 Contents 4 Chapter 1 Introduction 1 Chapter 2 Actuarial Cost Methods 5 2.1 Why and Wherefore > 2.2 Unit Credit 8 2.3. Entry Age Normal 16 2.4 More Entry Age Normal Jig 2.5. Individual Level Premium 25 2.6 Frozen Initial Liability 30 2.7 New Entrants 36 28 More Frozen Initial Liability 29 2.9 Aggregate 43 2.10 Pensioners 47 2.11 Pension Cost in Perspective 51 Chapter 3 Contributory Plans 53 ye Remarks 53 B74 Unit Credit 54 3.3 Entry Age Normal 58 3.4. Individual Level Premium 64 3.5 Entry Age Normal With Salary Scale 68 3.6 The Modified-Cash-Refund Annuity 72 ee Chapter 4 Ancillary Benefits 77 eeee SeS ee 4.1 Ancillary to What? TE 4.2 Vesting — Unit-Credit Method 78 4.3 A Note About Multiple-Decrement Theory 83 4.4 Vesting — Entry-Age-Normal Method 86 4.5 Early Retirement 89 4.6 Late Retirement 92 4.7. Retirement as an ‘‘Ancillary Benefit” 94 4.8 Other Ancillary Benefits Dy, Chapter 5 Assets 102 Syol What Are They? 102 5.2 Smoothed Market Value 107 5.3 The New-Money Method 114 5.4. Group Annuity Contracts i ey 5.5 Individual Life-Insurance Policies 126 5.6 The Big Picture 128 Chapter 6 Assumptions 131 6.1. Actuarial Science vs. ActuariaAlr t 13] 6.2 An Actuarial Paradox 132 6.3. The Service Table 139 6.4 Secondary Decrements 150 6.5 Interest, Inflation, and Salary Increases : 162 Chapter 7 Cost Methods Again 170 Gok Who Should Be Included? 170 7.2 More Unit Credit 185 7.3. More Individual Level Premium 195 Acknowledgements 207 Index to Principal Notation 208