On Cooperative Game Approaches For Optimal Portfolio Selection

Abstract

Cooperative game theory is concerned with exploring schemes for allocating payoffs among rational participants in coalitions and has produced several solution designs due to the different emphasis on criteria such as stability and fairness, but this theory has not been widely applied in the field of portfolio selection. In this paper, we explore further applications of the solution concepts of cooperative games based on the model of optimal portfolio selection developed in previous studies, which is modelled in a static form of a non-cooperative zero-sum game between investors and the market and a cooperative game between investors. We propose a risk modified Shapley value based on the tradeoff between return and risk in the financial market based on the Shapley value, and the performance of this solution shows an evident improvement. We also introduce some other solution concepts of cooperative games and give an approach to construct a nucleolus-based portfolio using Maschler's scheme to compute the nucleolus, and the results demonstrate that the allocation schemes based on the cooperative game theory perform well.