Multi-objective stochastic programming for portfolio selection

Abstract Generally, in the portfolio selection problem the Decision Maker (DM) considers simultaneously conflicting objectives such as rate of return, liquidity and risk. Multi-objective programming techniques such as goal programming (GP) and compromise programming (CP) are used to choose the portfolio best satisfying the DM’s aspirations and preferences. In this article, we assume that the parameters associated with the objectives are random and normally distributed. We propose a chance constrained compromise programming model (CCCP) as a deterministic transformation to multi-objective stochastic programming portfolio model. CCCP is based on CP and chance constrained programming (CCP) models. The proposed program is illustrated by means of a portfolio selection problem from the Tunisian stock exchange market.

[1]  J Figueira,et al.  Stochastic Programming , 1998, J. Oper. Res. Soc..

[2]  P. Lang,et al.  Dominance and Efficiency in Multicriteria Decision under Uncertainty , 1999 .

[3]  George C. Philippatos,et al.  GOAL PROGRAMMING AND THE SELECTION OF PORTFOLIOS BY DUAL-PURPOSE FUNDS , 1978 .

[4]  W. Ziemba,et al.  Worldwide asset and liability modeling , 1998 .

[5]  A. Charnes,et al.  Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints , 1963 .

[6]  Tsong-Yue Lai.  Portfolio selection with skewness: A multiple-objective approach , 1991 .

[7]  Wlodzimierz Ogryczak,et al.  Multiple criteria linear programming model for portfolio selection , 2000, Ann. Oper. Res..

[8]  Ralph E. Steuer,et al.  Multiple criteria decision making combined with finance: A categorized bibliographic study , 2003, Eur. J. Oper. Res..

[9]  Sang M. Lee,et al.  Goal programming for portfolio selection , 1980 .

[10]  P. Samuelson.  The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments , 1970 .

[11]  Milan Zelany,et al.  A concept of compromise solutions and the method of the displaced ideal , 1974, Comput. Oper. Res..

[12]  M. Padberg,et al.  Simple Criteria for Optimal Portfolio Selection , 1976 .

[13]  Chun-Hao Chang,et al.  Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets , 2003 .

[14]  Mehrdad Tamiz,et al.  A Two Staged Goal Programming Model for Portfolio Selection , 1996 .

[15]  Carlos Romero,et al.  Portfolio Selection: A Compromise Programming Solution , 1996 .

[16]  A. Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[17]  W. Sharpe.  A Simplified Model for Portfolio Analysis , 1963 .

[18]  Chue Shing,et al.  Interactive decision system in stochastic multiobjective portfolio selection , 1999 .

[19]  Fouad Ben Abdelaziz,et al.  Decision-maker's preferences modeling in the stochastic goal programming , 2005, Eur. J. Oper. Res..

[20]  Enrique Ballestero,et al.  Stochastic goal programming: A mean-variance approach , 2001, Eur. J. Oper. Res..

[21]  Pascal Lang,et al.  Distributional Efficiency in Multiobjective Stochastic Linear Programming , 1995 .

[22]  Nikolaos V. Sahinidis,et al.  Optimization under uncertainty: state-of-the-art and opportunities , 2004, Comput. Chem. Eng..

[23]  Howard Raiffa,et al.  Decision Making: RISKY CHOICE REVISITED , 1988 .

[24]  Constantin Zopounidis,et al.  Stock Evaluation Using a Preference Disaggregation Methodology , 1999 .

[25]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[26]  H. Levy.  Stochastic dominance and expected utility: survey and analysis , 1992 .

[27]  A. P. Muhlemann,et al.  PORTFOLIO MODELING IN MULTIPLE‐CRITERIA SITUATIONS UNDER UNCERTAINTY , 1978 .

[28]  W. Sharpe.  A Linear Programming Algorithm for Mutual Fund Portfolio Selection , 1967 .

[29]  David N. Nawrocki,et al.  Earnings announcements and portfolio selection. Do they add value , 1998 .

[30]  D. E. Bell,et al.  Decision making: Descriptive, normative, and prescriptive interactions. , 1990 .

[31]  Liping Liu,et al.  Approximate portfolio analysis , 1999, Eur. J. Oper. Res..

[32]  Fred D. Arditti.  RISK AND THE REQUIRED RETURN ON EQUITY , 1967 .

[33]  Ben Abdelaziz Foued,et al.  Application of goal programming in a multi-objective reservoir operation model in Tunisia , 2001, Eur. J. Oper. Res..

[34]  Abraham Charnes,et al.  Optimal Estimation of Executive Compensation by Linear Programming , 1955 .