Pension Fund Management Using the Markov Chain Approximation

Abstract

Funding policy and portfolio selection are two crucial issues in pension fund management. Merton (1969, 1971) initially explores these problems in a continuous time framework by constructing the Hamilton-Jacobi-Bellman (HJB) equations. This type of approach becomes complicated when control constraints are incorporated under an incomplete market. In this paper, we suggest using the Markov chain approximation methods proposed by Kushner and Dupuis (1992) to obtain the optimal solutions numerically. Monitoring mechanism linking plausible scenarios and numerical solutions are employed to scrutinize the contributions and asset allocations for defined benefit pension schemes. In the numerical illustration, we estimate the optimal strategies within a simplified two-asset opportunity set. The results show that the plan turnovers, the initial fund levels, and the time horizon heavily influence the optimal strategies.