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

Authors : Charles İ NKEKI

Pages : 219-244

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Publication Date : 2015-10-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(DC); pension scheme. The surplus, which is discounted, is solved with dynamic programming techniques. The pension plan member insert ignore into journalissuearticles values(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