An Optimal Portfolio Problem of DC Pension with Input-Delay and Jump-Diffusion Process

Abstract

In this paper, an optimal portfolio control problem of DC pension is studied where the time interval between the implementation of investment behavior and its effectiveness (hereafter input-delay) is particularly focused. There are two assets available for investment: a risk-free cash bond and a risky stock with a jump-diffusion process. And the wealth process of the pension fund is modeled as a stochastic delay differential equation. To secure a comfortable retirement life for pension members and also avoid excessive risk, the fund managers in this paper aim to minimize the expected value of quadratic deviations between the actual terminal fund scale and a preset terminal target. By applying the stochastic dynamic programming approach and the match method, the optimal portfolio control problem is solved and the closed-form solution is obtained. In addition, an algorithm is developed to calculate the numerical solution of the optimal strategy. Finally, we have performed a sensitivity analysis to explore how the managers’ preset terminal target, the length of input-delay, and the jump intensity of risky assets affect the optimal investment strategy.