Optimal strategies for collective defined contribution plans when the stock and labor markets are co-integrated

This paper investigates a collective defined contribution (CDC) pension fund scheme in continuous time, where members' contributions are fixed in advance, and benefit payments depend on the final salary rate. We take account of the co-integration between labor income and the stock market by letting the difference between logs of labor and dividends follow a mean-reverting process. Further, labor income is also a product of aggregate labor income and member's idiosyncratic shocks whose constant growth rate is unknown. It can be modeled by a continuous-time two-state hidden Markov chain. Further, the pension fund can be invested in the financial market consisting of one risky asset and one risk-free asset to enhance profits. After using Hamilton-Jacobi-Bellman (HJB) equations, the closed-form solutions for the optimal asset allocation and the benefit payment policies are obtained to maximize the social welfare and the terminal surplus wealth. Numerical examples are also conducted to illustrate the sensitivity of parameters on the optimal strategies.