Abstract

OPTIMAL ASSET ALLOCATION POLICY FOR A DEFINED CONTRIBUTION PENSION FUND WITH REFUND CLAUSE OF PREMIUM WITH PREDETERMINED INTEREST UNDER HESTON?S VOLATILITY MODEL

1 Osu, B. O 2Akpanibah, E. E. & 3Oruh, B. I.

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Abstract We study optimal asset allocation policy for a Defined Contribution (DC) pension fund with refund of premium clauses under Heston?s volatility model using mean-variance utility function. In this model, death members? next of kin are allowed to withdraw their member?s accumulations with predetermined interest. Next, we considered investments in one risk free asset (cash) and a risky asset (equity) to help increase the accumulated funds of the remaining members to meet their retirement needs. Also, the actuarial symbol is used to formulize the problem as a continuous time mean-variance stochastic optimal control problem. We establish an optimization problem from the extended Hamilton Jacobi Bellman equations using the game theoretic approach and solve the optimization problem to obtain the optimal allocation strategy for the two assets and also the efficient frontier of the pension members. Furthermore, we analysenumerically the effect of some parameters on the optimal allocation strategy. We deduce that as the initial wealth, predetermined interest rate, voluntary contribution and risk averse level increases, the optimal allocation policy for the risky asset (equity) decreases. Keywords: DC pension fund,extended HJB equation, optimal allocation policy, refund of contribution clause, interestrate.

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