Abstract
In this paper, we apply the stochastic optimal control theory to the pension fund management before and after retirement in the defined contribution and defined benefit pension schemes, where benefits are paid as investment returns for a period or duration of time. The goal of the management problem is to optimize the long-term growth of expected utility of returns. We consider different types of power law utility function of the form U(X)=γ-1Xγ, γ<1, γ≠0 to examine the different investment schemes. Our result shows the advantage of the defined contribution scheme over the defined benefit scheme before and after retirement.
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