Multi-Objective Optimization Research In Portfolio Selection

Portfolio selection problem is essentially a multi-objective optimal problem which contains two goals, one goal is to achieve maximization of expected revenue, another goal is to realize risk minimization, and we call the multi-objective optimal problem as the original problem. In Markowitz's mean-variance model, the problem of single objective optimization was obtained with the expected revenue fixed, portfolio theory made great progress, especially the CAPM was the greatest achievement.Objective function of expected revenue was taken as the constraint condition in Markowitz's mean-variance model, so the mean-variance model was equivalent to the constraint method of the original problem. The author discussed the feasible region and efficient solution of the original problem, Capital Market Line Equation was solved by using the hyperbola that crossed the minimum and maximal expected revenue points as the efficient frontier, and the proportion coefficients of the market portfolio were calculated; The feasible region of the original problem was a convex set, the efficient solution of the equivalent model existed, the evaluation method was also feasible, these conclusions were significant for solving the problem; The author made a distinction between the indifference curve and the evaluation function, an indifference curve must be an evaluation curve, but an evaluation curve is not necessarily an indifference curve, based on some special indifference curve the proportion coefficients of optimal portfolio was simultaneously given by the form of formula.