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

• DOI: 10.1007/s13160-021-00481-z
• Publication Date: 2021-08-30T11:02:52Z
• Authors: Calisto Guambe; Rodwell Kufakunesu; Gusti van Zyl; Conrad Beyers
• Keywords: Jump Diffusion; Hamilton–Jacobi–Bellman equation; Value (mathematics)

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.