A Mathematical Model of Pension Fund Operation and Methods of Fund Stability Analysis

Abstract

We consider the probability of ruin of a pension fund on a finite time interval. The basis is provided by the standard Cramer–Lundberg model, which is modified by specifying enrolment and contribution parameters in the form of random variables. A number of factors may be treated as random variables in the model: the date of member’s death, members’ wages, the number of fund members, financial indicators (discounting and return rates, inflation, wage growth rates). Each of these factors specified as a random variable affects the nondeterministic behavior of the fund’s receipts and payouts. In this article, the random factors include the number of members joining the pension fund in the relevant year and random mortality.