The analytic approach for the stochastic projection of the public pension fund

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.