Optimal Control of Mutual Fund Portfolio Choice in the Presence of Dynamic Flow with Partial Information

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November 2016
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We study the utility maximization problem of an economic agent who maximizes the expected utility of the terminal value of his wealth resulting from an investment in a mutual fund and a risk-less asset over a finite time interval in a financial market with partial information. We use continuous-time ordinary differential equation and stochastic differential equation to model security prices. The novelty of this work is that we restrict the assumption that market participants can observe the drift vector process used in the specification of stochastic differential equation for the asset prices. Kalman-Bucy filtering method is used to estimate the drift vector process. Stochastic control theory and dynamic programming methods were used to address the maximization problem. The main results are the explicit representation of the optimal trading strategies and value functional for the economic agent and the fund manager for three different utility functions: namely, the log, power and negative exponential. The optimal trading strategies of the economic agent are independent of wealth level except for the negative exponential utility function whose optimal trading strategy is a decreasing function of wealth. They inversely related to the fee rate for all the utility functions. Optimal trading strategies for the fund manager are also autonomous of wealth level, but directly correlated to the fee rate charged. The accumulated fee process of the mutual fund is autonomous of the fee rate charged and directly related to wealth level (except for the negative exponential utility function where it is independent of wealth). We found that the product of the economic agent’s optimal trading strategy and the fund manager’s optimal trading strategy results in the optimal trading strategy that the economic agent would have selected if he had been allowed to trade freely in the risky securities.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of Master of Philosophy in Actuarial Science,