Optimal investment strategies for hybrid pension with common shock and risk-sharing

Abstract

This paper investigates the optimal investment problem for hybrid pension plans in a financial market with jump-diffusion risky assets, where both the contribution and the benefit are adjusted based on the plan’s performance, and risks are shared across different generations. The investment in a risk-free asset and two risky assets is carried out by the managers of the pension fund. The model of risky asset is assumed to be modulated by a compound Poisson process, with the two risky asset price processes correlated through a common shock. The objective of this study is to seek the optimal investment strategies and risk-sharing arrangements for plan trustees and participants that minimize the costs associated with unstable contribution risks, unstable benefit risks, and discontinuous risks. By applying the stochastic optimal control approach, the closed-form expressions of the optimal strategy and value function are derived. Numerical examples are provided to analyze the effects of parameters on the optimal strategies. In the context of the hybrid pension plan, these strategies effectively facilitate intergenerational risk-sharing.

Keywords

Hybrid pension / Intergenerational risk-sharing / Common shock / Jump-diffusion process / Hamilton-Jacobi-Bellman equation

Acknowledgements

This work is supported by the National Key R&D Program of China (Grant No. 2023YFA1009204).

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