Bargaining and Optimal Investments

Abstract

The optimal portfolio selection is one of the most investigated problem in Investment Theory. When randomness is introduced in return rates, one has to take into account the risk associated to each investment. The set of admissible portofolio becomes a two dimensional set and utility function has to be modified introducing risk which, in a rational market, is directly proportional to return. When it is possible to find a line of efficient portfolios the investor uses subjective preference to choose a particular point on it. The tools to tackle uncertain situation span from mathematical programming to stochastic optimal control, referring in any case to uniqueness of the decision maker. Aim of this paper is to imbed portfolio selection in a dynamic cooperative game framework and qualify the choice of an optimal portfolio as the corresponding bargaining solution.