Pension accumulation as a semi-Markov reward process, with applications to pension reform

  • Yves Balcer
  • Izzet Sahin


A fundamental point of departure of the economic analysis of savings by individuals is Samuelson’s consumption loan model. Although prevalent in the analysis of social security and saving behavior, this “representative consumer life cycle model” is inappropriate for the study of private (employment) pensions due to a number of important characteristics of these latter arrangements that distinguish them from social security. In addition to wage and benefit levels, accrual of employment pension benefits are based on the applicable vesting provisions (see below) and therefore on mobility. In addition, while the wage factors entered in social security benefit calculations are indexed until retirement, in the case of employment pensions there is either no indexing or only partial indexing until employment termination which may precede retirement by many years. It is well-known that these differences between the two systems have very important consequences in the face of high labor mobility, especially during periods of high wage growth. It is the interaction of labor mobility, inflation, and pension coverage and portability (see below) that results in an unequal distribution of pension benefits to individuals with comparable working lives and lifetime wage profiles. These characteristics are not reflected by the consumption loan model.


Pension Plan Pension Benefit Pension Reform Royal Commission Private Pension 
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  1. Balcer, Y. and I. Sahin (1979). Probabilistic Models for Pension Benefits, The Journal of Risk and Insurance, 46, 99–123.Google Scholar
  2. Balcer, Y. and I. Sahin (1980). A Study of Private Pensions in Ontario. Report of the Royal Commission on the Status of Pensions in Ontario. Volume 9: Background Studies and Papers, Government of Ontario, 151-207.Google Scholar
  3. Balcer, Y. and I. Sahin (1982). Modelling the Impact of Pension Reform — A Case Study The Journal of Risk and Insurance, 49, 158–191.CrossRefGoogle Scholar
  4. Balcer, Y. and I. Sahin (1983). A Stochastic Theory of Pension Dynamics. Insurance: Mathematics and Economics, 2, 179–197.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Balcer Y, and I. Sahin (1984). Dynamics of Pension Reform: The Case of Ontario. The Journal of Risk and Insurance, 51, 652–686.CrossRefGoogle Scholar
  6. Report of the Royal Commission on the Status of Pensions in Ontario. (1980), (9 volumes), Government of Ontario.Google Scholar
  7. Sahin, I. (1978). Cumulative Constrained Sojourn Times in Semi-Markov Processes with an Application to Pensionable Service. Journal of Applied Probability, 15, 531–542.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Sahin, I. (1984). Bruce’s Spider and the Employee’s Risk under a Pension System. The Journal of Risk and Insurance, 51, 143–149.CrossRefGoogle Scholar
  9. Sahin, I. and Y. Balcer (1979). Stochastic Models for Pensionable Service. Operations Research, 27, 888–903.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Yves Balcer
    • 1
  • Izzet Sahin
    • 2
  1. 1.Dept of EconomicsUniversity of Wisconsin-MadisonUSA
  2. 2.School of Business AdministrationUniversity of Wisconsin-MilwaukeeUSA

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