Decision Theory under Uncertainty Mean-Variance Approach

Abstract

In this paper, we mainly consider the theory and analysis of Decision under uncertainty which is making the foundations of all finance and portfolio theories. Decision makers face choices among a number of risky alternatives which is represented by lotteries. This paper develops alternative theories for choices under risk which expected utility theory which is derived from reasonable axioms about rational behavior in risky environment. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets. All risky alternatives can be summarized by two numbers – mean u and variance   called Mean-Variance Theory (MVT). This implies that typical mean-variance utility function v which is increasing in and decreasing in.The results show that, investors have different mean variance utility functions but the main results regarding optimal portfolio of risky assets do not depend on the specific utility functions of investors.