Time consistent mean-variance asset allocation for a DC plan with regime switching under a jump-diffusion model
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Date
Authors
Guambe, Calisto
Kufakunesu, Rodwell
Van Zyl, Gusti
Beyers, Conrad F.J.
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
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.
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Keywords
Hamilton-Jacobi-Bellman (HJB), DC pension plan, Mean-variance, Stochastic income, Regime-switching, Extended HJB, Mortality risks
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Citation
Guambe, C., Kufakunesu, R., van Zyl, G. et al. Time consistent mean-variance asset allocation for a DC plan with regime switching under a jump-diffusion model. Japan Journal of Industrial and Applied Mathematics 39, 119–143 (2022). https://doi.org/10.1007/s13160-021-00481-z.