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Manage Pension Deficit with Heterogeneous Insurance |
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| Authors: | Sheng De-Lei Shi Linfeng Li Danping Zhao Yanping |
| Institution: | 1.Faculty of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, 030006, China ;2.School of Finance, Shanxi University of Finance and Economics, Taiyuan, 030006, China ;3.Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, Faculty of Economics and Management, East China Normal University, Shanghai, 200062, China ; |
| Abstract: | 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. |
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