A New and Efficient Algorithm for a Class of Portfolio Selection Problems

This paper proposes a new approach and develops an efficient algorithm for solving a class of (simplified) portfolio selection problems. The approach is based on the technique of parametric principal pivoting. The algorithm is particularly suited for problems with special structure and can handle potentially large problems. When specialized to the multiple index model, the algorithm achieves enormous savings in computer storage and computations.

[1]  G. Dantzig,et al.  COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[2]  Ikuyo Kaneko THE PARAMETRIC LINEAR COMPLEMENTARITY PROBLEM IN THE DE DONATO-MAIER ANALYSIS OF REINFORCED CONCRETE BEAMS , 1975 .

[3]  H. Samelson,et al.  A partition theorem for Euclidean $n$-space , 1958 .

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

[5]  R. Sargent,et al.  An efficient implementation of the Lemke algorithm and its extension to deal with upper and lower bounds , 1978 .

[6]  Barr Rosenberg and Andrew Rudd. Portfolio Optimization Algorithms: A Progress Report , 1976 .

[7]  Jong-Shi Pang,et al.  On a class of least-element complementarity problems , 1979, Math. Program..

[8]  Manfred W. Padberg,et al.  Simple Criteria for Optimal Portfolio Selection with Upper Bounds , 1977, Oper. Res..

[9]  P. Morse,et al.  Principles of Numerical Analysis , 1954 .

[10]  Balder Von Hohenbalken,et al.  A finite algorithm to maximize certain pseudoconcave functions on polytopes , 1975, Math. Program..

[11]  Robert L. Graves,et al.  A Principal Pivoting Simplex Algorithm for Linear and Quadratic Programming , 1967, Oper. Res..

[12]  W. Sharpe Portfolio Theory and Capital Markets , 1970 .

[13]  P. Gill,et al.  Methods for computing and modifying the $LDV$ factors of a matrix , 1975 .

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

[15]  B. A. Murtagh,et al.  Projection methods for non-linear programming , 1973, Math. Program..

[16]  J. Pang,et al.  On the Solution of Some (Parametric) Linear Complementarity Problems with Applications to Portfolio Analysis, Structural Engineering and Graduation. , 1977 .

[17]  Manfred W. Padberg,et al.  Simple Rules for Optimal Portfolio Selection: The Multi Group Case , 1977, Journal of Financial and Quantitative Analysis.

[18]  Ikuyo Kaneko,et al.  A linear complementarity problem with an n by 2n “P”-matrix , 1978 .

[19]  B. Stone A Linear Programming Formulation of the General Portfolio Selection Problem , 1973, Journal of Financial and Quantitative Analysis.

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