Optimal investment strategy for the DC pension plan based on jump diffusion model and S-shaped utility

Abstract

In this paper, we study the optimal investment strategy for a defined contribution pension plan under the jump diffusion model and S-shaped utility. We assume that pension plan members can invest their pension fund in the financial market consisting of a risk-free asset and a risk asset whose price process follows a jump diffusion process. The goal of pension plan managers is to maximize the expected utility of the real terminal wealth under the jump diffusion model and S-shaped utility. We apply Lagrange dual method, concavification technique and martingale method to derive the closed-form expressions of the optimal wealth process and the optimal investment strategy. Finally, we also try to use some numerical analysis to explain the impacts of model parameters on the optimal terminal wealth value and trading strategy.