Stochastic pension fund modelling

A. J G Cairns, Gary Parker

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


This paper considers the stochastic behaviour of the funding level of a defined benefit pension plan through time and its relationship with the plan contribution rate. First, we investigate the effect of the valuation basis and of the amortization period on the variability of funding levels and contribution rates and this introduces the concept of the efficient frontier as a means of choosing an optimal funding strategy. Second, we consider models with dependent rates of return and provide a sufficient condition for the funding level to be ergodic. Upon considering the AR(1) model we derive a recursive method for calculating the conditional distribution of the funding level and provide further insight into the main factors which influence the behaviour of the funding level. © 1997 Elsevier Science B.V.

Original languageEnglish
Pages (from-to)43-79
Number of pages37
JournalInsurance: Mathematics and Economics
Issue number1
Publication statusPublished - 30 Oct 1997


  • Ar(1) model
  • Conditional distribution
  • Efficient frontier
  • Ergodic theorem
  • Stochastic rates of return
  • Valuation rate of interest


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