Edikan E. Akpanibah1;2, Bright O. Osu1, Ben I. Oruh1, Okonkwo C. Ukwuoma1;3 and Everestus O. Eze1

In this work, how investment portfolios of a pension scheme can be maximized in the presence of return clause of
contributions is presented. This clause permits return of accumulated contributions together with predetermined
interest from risk free asset to members’ families whenever death occurs to their family members. Also considered
herein are investments in cash, marketable security and loan to increase the total accumulated funds of the pension
scheme left to be distributed among the surviving members such that the price models of marketable security and
loan follows geometric Brownian motions. The game theoretic approach, separation of variable technique and mean
variance utility are used to obtain closed form solutions of the optimal control plans for the assets and the efficient
frontier. Next, the consequence of some parameters on the optimal control plans with time is numerically analysed.
Furthermore, a theoretical comparison of our result with an existing result is given.


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