Operation Research Techniques in Portfolio Optimization

Design of financial portfolios which are optimal, in the sense of having maximum return or minimum risk, is a fundamental problem in the financial markets. In this paper we discuss various portfolio optimization problems and present their solutions in the framework of operation research techniques. We also discuss a very important duality property that these problems possess.This paper aims at a systematic presentation of operation research techniques and methodology employed to optimize portfolios subject to various constraints. It is important to note that all the procedures described are readily programmable on computer, so the optimal portfolios can be quickly computed.The objective of an investor might primarily be having a portfolio with the highest achievable return. We discuss and solve the problems of unconstrained maximized-return portfolio optimization, maximized-return portfolio optimization with a target risk, and maximized-return portfolio optimization with a target upper bound on risk.The objective of an investor might primarily be having a portfolio with the lowest achievable risk. We discuss and solve the problems of unconstrained minimized-risk portfolio optimization, minimized-risk portfolio optimization with a target return, and minimized-risk portfolio optimization with a target lower bound on return.Finally, we discuss a very important duality property of the optimization problems of return maximization and risk minimization

کلیدواژه ها:

portfolio optimization ، portfolio risk ، financial planning ، duality