tailieunhanh - Portfolio Optimization: Some aspectsof modeling and computing

The paper focuses on computational aspects of portfolio optimization (PO) problems. The objectives of such problems may include: expectedreturn, standard deviation and variationcoefficient of the portfolioreturn rate. | VNU Journal of Science: Policy and Management Studies, Vol. 33, No. 2 (2017) 1-9 RESEARCH Portfolio Optimization: Some Aspects of Modeling and Computing Nguyen Hai Thanh*, Nguyen Van Dinh VNU International School, Building G7-G8, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam Received 20 April 2017 Revised 10 June 2017, Accepted 28 June 2017 Abstract: The paper focuses on computational aspects of portfolio optimization (PO) problems. The objectives of such problems may include: expectedreturn, standard deviation and variation coefficient of the portfolioreturn rate. PO problems can be formulated as mathematical programming problems in crisp, stochastic or fuzzy environments. To compute optimal solutions of such single- and multi-objective programming problems, the paper proposes the use of a computational optimization method such as RST2ANU method, which can be applied for nonconvex programming problems. Especially, an updated version of the interactive fuzzy utility method, named UIFUM, is proposed to deal with portfolio multi-objective optimization problems. Keywords: Portfolio optimization, mathematical programming, single-objective optimization, multi-objective optimization, computational optimization methods. 1. Introduction * combinations of investments offer both lower expected risk and higher expected return than other combinations. Modern portfolio theory also shows that certain combinations only offer increased reward with increased risk. This set of combinations is referred to as the efficient frontier [1]. In this paper, the classical PO problem is considered: There are k assets (stocks)for possible investment. For each asset i with return rate Ri, i = 1, 2, ,k, expected return i= E(Ri) Modern portfolio theory, fathered by Harry Markowitz in the 1950s, assumes that an investor wants to maximize a portfolio's expected return contingent on any given amount of risk, with risk measured by the standard deviation of the portfolio's return rate. For portfolios .