This paper considers a positive and increasing pension deficit of a certain pay-as-you-go (PAYG) pension system, and tries to make up for this deficit by using heterogeneous insurance. The positive pension deficit is formulated as a mathematical function in continuous time. The surplus of an appropriate heterogeneous insurance is described by diffusion approximation of a Cramér-Lundberg process. The system of extended Hamilton-Jacobi-Bellman equations under mean-variance criterion is established. The closed-form solution and optimal surplus-multiplier of heterogenous insurance are obtained. Some interpretations further explain the theoretical values of the results.

本文考虑了一种现收现付制（PAYG）养老金制度的正向且不断增加的养老金赤字，并试图通过使用异质保险来弥补这一赤字。正养老金赤字被表述为连续时间的数学函数。适当异质保险的盈余通过 Cramér-Lundberg 过程的扩散近似来描述。建立了均方差准则下的扩展Hamilton-Jacobi-Bellman方程组。得到了异质保险的闭式解和最优剩余乘数。一些解释进一步解释了结果的理论值。