A note on a minimax rule for portfolio selection and equilibrium price system

This paper concerns a minimax model to investigate the optimal portfolio selection problem without riskless assets and with or without short sale restriction. A numerical solution to the problem with short sale restriction is obtained by using the maximum entropy algorithm. For the problem without short sale restriction, we derive a analytical expression for the optimal solution, a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system, and an explicit formula for the price system. Furthermore, a numerical example is given to show the validity of the method.

[1]  Hiroshi Konno,et al.  EXISTENCE OF A NONNEGATIVE EQUILIBRIUM PRICE VECTOR IN THE MEAN‐VARIANCE CAPITAL MARKET , 1995 .

[2]  H. Konno,et al.  A MEAN-VARIANCE-SKEWNESS PORTFOLIO OPTIMIZATION MODEL , 1995 .

[3]  James C. T. Mao,et al.  Models of Capital Budgeting, E-V VS E-S , 1970, Journal of Financial and Quantitative Analysis.

[4]  Kok Lay Teo,et al.  Portfolio Optimization Under a Minimax Rule , 2000 .

[5]  Wanhua Qiu,et al.  A measure of risk and a decision-making model based on expected utility and entropy , 2005, Eur. J. Oper. Res..

[6]  Byung Ha Lim,et al.  A Minimax Portfolio Selection Rule with Linear Programming Solution , 1998 .

[7]  Arun J. Prakash,et al.  Portfolio selection and skewness: Evidence from international stock markets , 1997 .

[8]  H. Konno,et al.  Equilibrium relations in a capital asset market: A mean absolute deviation approach , 1994 .

[9]  Xiaotie Deng,et al.  A minimax portfolio selection strategy with equilibrium , 2005, Eur. J. Oper. Res..

[10]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[11]  Yan Gao,et al.  An algorithm for portfolio selection in a frictional market , 2006, Appl. Math. Comput..

[12]  H. Konno.  Equilibrium Relation in the Mean-Absolute Deviation Capital Market , 1994 .

[13]  Hiroshi Konno,et al.  Minimal concave cost rebalance of a portfolio to the efficient frontier , 2003, Math. Program..

[14]  H. Konno,et al.  Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market , 1991 .

[15]  Shouyang Wang,et al.  A minimax rule for portfolio selection in frictional markets , 2003, Math. Methods Oper. Res..

[16]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[17]  Henk Grootveld,et al.  Variance vs downside risk: Is there really that much difference? , 1999, Eur. J. Oper. Res..

[18]  Fouad Ben Abdelaziz,et al.  Multi-objective stochastic programming for portfolio selection , 2007, Eur. J. Oper. Res..

[19]  Yusif Simaan.  Estimation risk in portfolio selection: the mean variance model versus the mean absolute deviation model , 1997 .

[20]  Kin Keung Lai,et al.  Optimal Consumption Portfolio and No-Arbitrage with Nonproportional Transaction Costs , 2005, Ann. Oper. Res..

[21]  Kok Lay Teo,et al.  Portfolio Selection Problem with Minimax Type Risk Function , 2001, Ann. Oper. Res..