Abstract

This paper studies the optimal investment and benefit adjustment problem for a collective DC pension plan under longevity trend. We assume that the mortality hazard rate is a function of age and time, which extend the Makeham's Law and can describe the longevity trend. The contribution rate is a predetermined proportion of average salary while the benefit payments depends on the pension wealth. The pension fund is allowed to invest in a risk-free asset and a risky asset whose price process satisfies the CEV model. The objective is expected utility maximization of terminal wealth and cumulative weighted product of benefit and wealth. By applying dynamic programming approach, we establish the corresponding Hamilton-Jacobi-Bellman equation and obtain the optimal investment and benefit strategies for CARA and CRRA utilities, respectively. Finally, numerical example is provided to analyze the effects of parameters on the optimal strategies. The results show that under the CARA utility function, only the optimal benefit strategy is related to longevity trend, while under the CRRA utility function, longevity trend has effects on both the optimal benefit and investment strategies.