OPTIMAL SURPLUS, MINIMUM PENSION BENEFITS AND CONSUMPTION PLANS IN A MEAN-VARIANCE PORTFOLIO APPROACH FOR A DEFINED CONTRIBUTION PENSION SCHEME

Abstract

In this paper, we study the problem of simultaneous maximization of the value of expected terminal surplus and, minimization of risks associated with the terminal surplus in a de ned contribution (DC) pension scheme. The surplus, which is discounted, is solved with dynamic programming techniques. The pension plan member (PPM) makes a ow of contributions from his or her stochastic salary into the scheme. The ow of contributions are invested into a market that is characterized by a cash account, an index bond and a stock. The ecient frontier for the discounted and real surplus are obtained. Optimal consumption of the PPM was found to depend on the terminal wealth, random evolution of minimum pension bene t and "variance minimizing" parameter. It was found that as the variance minimizing parameter, tends to zero, the op- timal consumption tends to negative in nity. The optimal expected discounted and real surplus, optimal total expected pension bene ts and expected min- imum pension bene ts were obtained. We found that the optimal portfolio depends linearly on the random evolution of PPM's minimum bene ts. Some numerical examples of the results are established.

Keywords

• pension scheme,mean-variance,stochastic funding,dened contribution,ecient frontier,surplus,minimum pension benets,optimal consumption

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