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The essence of this work is to study the optimal investment policy in a defined contribution pension scheme with return clause of contributions under volatility risks. In our model, the pension fund managers are mandated to return the accumulated contributions of members who die during the accumulation phase to their next of kin. Also, investment in one risk free asset and two risky assets (stock and loan) are considered such that the stock market price is driven by Heston volatility model and the remaining accumulations are distributed among the remaining members. Using mean variance utility function, game theory and variable separation technique, a closed form solution of the optimal investment policy, the optimal fund size and the efficient frontier were obtained. Furthermore, a sensitivity analysis of the effects of some parameters on the optimal investment policies and efficient frontiers were carried out theoretically.

Optimal Investment Policy in a Pension Fund System with Return Clause and Multiple Assets under Volatility Risks