Portfolio Selection Strategies with Return Clause in a DC Pension Fund
Edikan E. Akpanibah *
Department of Mathematics and Statistics, Federal University Otuoke, P.M.B. 126, Bayelsa, Nigeria.
Udeme O. Ini
Department of Mathematics and Computer Science, Niger Delta University, Bayelsa, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper solves the problem faced by a pension fund manager in determining the optimal selection strategies involving four different assets comprising of one risk free asset and three risky assets whose prices are modelled by geometric Brownian motion. Also, a clause mandating the fund managers to return the accumulations with predetermined interest to members who lost their life during the accumulation period is considered. A stochastic optimal control model is formulated comprising of member’s monthly contributions, invested funds and the returned contributions. Also, an optimization problem from the extended Hamilton Jacobi Bellman (HJB) equation is established using the game theoretic approach. The explicit solutions of the optimal selection strategies and the efficient frontier are obtained by solving the extended HJB equation using the mean variance utility and separation of variable technique. Furthermore, a sensitivity analysis of the effect of some parameters on the optimal selection strategies is carried out numerically.
Keywords: DC pension fund, extended HJB equation, optimal investment strategies, game theoretic approach, return clause, Geometric Brownian motion.