Application of Game Theory in Optimal Portfolio Selection

Abstract

Finance is concerned with how savings from investors are distributed to businesses via financial markets and middlemen, who then utilize them to fund their activities. After the inclusion of asset pricing’s uncertainty, it was discovered that older analysis could not explain many aspects of corporate finance. Game theory is that part of applied mathematics that is concerned with how agents communicate with each other through their choices. It has developed a framework that has contributed to extra knowledge into many unknown phenomena, giving chance for the inclusion of asymmetric knowledge and strategic engagement. In this study, a computational study and application of Game Theory Model to investment decisions in an optimal portfolio selection problem are considered. Emphasis was placed on an investment decision problem using data from Invest, Grow, Secure (IGS) Financial Services for the year 2018. The decision-maker had to select at least one option from all possible options provided by IGS Financial Services in which an investment was made. The problem was to decide what action or a combination of actions to take among the various possible options with the given rates of return. The study was successful in modeling investment options of investors as a Game Theoretic Mathematical Problem that maximizes the returns from their investments. The application of Game Theory in the financial investment strategy is also successful in offering an optimal solution as opposed to an investor's personal discretionary means. Hence, the investor is able to make better investment policies decisions based on which combinations of payoff is providing the optimal value of returns. Furthermore, the results from the maximization of returns showed that, allocating 20 percent and 50 percent of the investor’s funds in the first quarter and second quarter respectively, yielded the maximum returns to the investor. The results from the minimization of cost however, showed that, allocating 70% of the investor’s funds in a 12 months investment policy, minimizes the most cost to the company.