In this paper, we propose a stochastic method to project the public pension fund in the public pension system (PPS). For this we introduce the stochastic differential equations for the three parts: the premium revenue, the benefit expenditure, and the fund process. From these we show that the solution of the aggregated fund process is the sum of log-normals, which is approximated as one log-normal for the analytic result. Related to the parameter estimations, we implement the moment matching in the first moment. For the second moment, we apply the extreme value method following Parkinson. In order to follow Parkinson, we take the maximum and the minimum range of the fund amount based on the various sensitivity result as well as the baseline one from the deterministic projection result. In this reason, it is naturally to maintain the close interrelation with the deterministic projection result, which is very important since it is still key result in the actuarial valuation of the PPS.

An aging population in modern societies has put stress on public pension systems. To prevent social security deficits from increasing to unbounded levels of public debt we focus on two policies: reducing the generosity of pension benefits, determined by the government, and postponing the effective retirement age, chosen by employees. An atomistic employee would disregard the effect of his retirement decision on the public debt and would retire as soon as possible. Conversely, an ideal farsighted agency considering all current and future employees would postpone retirement, thereby alleviating the pressure on public debt and allowing a more generous long-run pension. The government may design a proper incentive strategy to induce myopic atomistic decision makers to act nonmyopically. This strategy is a two-part incentive with nonlinear dependence on the stock of public debt. It is credible if deceiving employees slightly adjust their retirement-age decisions to increments in the public debt.