Pension Mathematics for Actuaries

232 Pages·1992·10.186 MB·English

by  Arthur W. Anderson

ISBN: 0-936031-10-7
PENSION MATHEMATICS _
_ FOR ACTUARIES
Second Edition _
ArihurW . Anderson

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in 2021 with funding from
Kahle/Austin Foundation ©
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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