Time consistent mean-variance asset allocation for a DC plan with regime switching under a jump-diffusion model

In this paper, we study a time consistent solution for a defined contribution pension plan under a mean-variance criterion with regime switching in a jump-diffusion setup, during the accumulation phase. We consider a market consisting of a risk-free asset and a geometric jump-diffusion risky asset process. Our solution allows the fund manager to incorporate a clause which allows for the distribution of a member’s premiums to his surviving dependents, should the member die before retirement. Applying the extended Hamilton-Jacobi-Bellman (HJB) equation, we derive the explicit time consistent equilibrium strategy and the value function. We then provide some numerical simulations to illustrate our results.The University of Pretoria ABSA Chair in Actuarial Sciencehttp://link.springer.com/journal/131602022-08-30hj2022Insurance and Actuarial ScienceMathematics and Applied Mathematic