Abstract

RETURN OF CONTRIBUTION CLAUSE IN A DC PLAN UNDER MODIFIED CEV MODEL

Ini, U. O.1 and Akpanibah, E. E.2*

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In this research paper, a defined contribution (DC) pension plan member?s optimal portfolio strategy with return of contribution clause under modified constant elasticity of variance (M-CEV) is studied. Considering investment in a risk- free asset and a risky asset modeled by a M-CEV process, a continuous time mean-variance stochastic optimal control problem consisting of members? monthly contributions, returned contributions and invested funds is formulated. Using the game theoretic method and mean variance utility, a non-linear partial differential equation (PDE) called the extended Hamilton Jacobi Bellman (HJB) is established and solved for the optimal portfolio strategy and efficient frontier using change of variable and variable separation technique. Also, theoretical analyses of the impact of the modification parameter and some other sensitive parameters on the optimal portfolio strategy were studied. Moreover, our result generalizes some existing results. Keywords: Modified constant elasticity of variance, extended HJB equation, optimal portfolio strategy, return of contribution, mean variance utility, change of variable technique.

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