OPTIMAL INVESTMENT AND OPTIMAL ADDITIONAL VOLUNTARY CONTRIBUTION RATE OF A DC PENSION FUND IN A JUMP-DIFFUSION ENVIRONMENT

Abstract

This paper considers an optimal investment and an optimal additional contribution rate of a pension plan member (PPM) who faces both diffusion and jump risks in a defined contribution (DC) pension plan. We put into consideration three background risks which include interest rate, investment and salary risks. The stock prices, interest rate and salary process of a PPM are allowed to follow a jump-diffusion process. A PPM is expected to make two kind of contributions: compulsory and additional voluntary contributions. The compulsory one is a fixed proportion of a PPM's salary and the additional one is voluntary which is time and interest rate dependent. The aims of the investor is to determine the optimal investment and optimal contribution rate in a jump-diffusion environment. In order to obtain the optimal investment and optimal contribution rate, the resulting wealth process was transformed into Hamilton–Jacobi–Bellman equation by the method of dynamic programming. As a result, the optimal investment and optimal contribution rate of a PPM were obtained. Furthermore, some empirical analyses were conducted and results obtained. We found that the optimal investment ultimately depend on stocks diffusion and jump risks, interest rate and salary risks, optimal contribution rate and the salary process. The contribution rate of a PPM was found to depend on the investment strategies, salary process and interest rate risks, salary and its growth rate and CRRA coefficient. We also found that the contribution rate depends inversely on the salary process of a PPM over time.