  Defined-contribution Pension Reinsurance and Investment Game of Non-zero-sum Utilizing Jump-diffusion and Heston Models

Abstract

In response to global aging challenges, establishing a sustainable pension investment management system has become crucial. This study proposes a defined-contribution (DC) pension risk mitigation framework that integrates investment and reinsurance strategies. Within this framework, we construct an investment game model of non-zero-sum for two pension investors with wealth maximization goals, allowing allocations to risk-free assets, risky assets, and reinsurance contracts. The higher-risk assets' time-varying market risk is modeled using the HestonModel whichis characterized by stochastic volatility with mean-reversion. And the reinsurance surplus is denoted by a jump-diffusion model to capture the sudden financial shocks. Moreover, by utilizing standard dynamic programming and exponential utility preferences, we can derive a closed solution to the investment strategy throughout mathematical proofs. Our new model innovatively combines jump-diffusion processes with stochastic volatility from the Heston Model, expanding the theoretical foundation for pension investment optimization strategies. Practically, it offers pension managers a dynamic asset allocation tool which can increase portfolios' resistance to systemic risks.