Principles of Optimization for Portfolio Selection

Abstract

The mathematical theory of optimization has a natural application in the field of finance. From a general perspective, the behavior of economic agents in the face of uncertainty involves balancing expected risks and expected rewards. For example, the portfolio choice problem concerns the optimal trade-off between risk and reward. A portfolio is said to be optimal in the sense that it is the best portfolio among many alternative ones. The criterion that measures the quality of a portfolio relative to the others is known as the objective function in optimization theory. The set of portfolios among which we are choosing is called the “set of feasible solutions” or the “set of feasible points.” Keywords: optimization; set of feasible solutions; constraint set; objective function; linear problems; quadratic problems; convex problems; unconstrained optimization; saddle point; optimal; convex functions; function; functional; concave; quasi-convex functions; quasi-concave; set of feasible points; constraint set; Lagrange multipliers; convex programming; set of feasible points; linear programming; quadratic programming; Lagrange multipliers; Lagrangian