Assets allocation strategy in a DC pension scheme with refund clause of contributions with predetermined interest under Heston’s Volatility model

Abstract

We studied asset allocation strategy in a defined contribution (DC) pension plan with refund contribution clauses under Heston's Volatility model using  mean-variance utility function. We assumed that the refund contributions are with predetermined interest and considered investments in cash and equity to help increase the accumulated funds of the remaining members to meet their retirement needs. Also, the actuarial symbol is used to formalize the problem as a continuous time mean-variance stochastic optimal control problem. We established an optimized problem from the extended Hamilton Jacobi Bellman equations and solved the optimized problem and obtained the optimal allocation strategy for the two assets and also the efficient frontier of the pension members. Furthermore, we analysed numerically the effect of some parameters on the optimal allocation strategy. We deduced that as the initial wealth, predetermined interest rate, and risk averse level increases, the optimal allocation strategy for equity decreases.

Keywords: DC Pension Fund, HJB, optimal allocation strategy, Refund of contribution clause, Interest Rate.