Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem

2000 ◽  
Vol 111 (1) ◽  
pp. 3-28 ◽  
Author(s):  
Masahiro Inuiguchi ◽  
Jaroslav Ramı́k
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Stochastic Programming ◽  
Portfolio Selection ◽  
Selection Problem ◽  
Fuzzy Mathematical Programming ◽  
Portfolio Selection Problem ◽  
Possibilistic Linear Programming

HIERARCHICAL DECISION MAKING IN STRATEGIC INVESTMENT BY A BOLTZMANN MACHINE

1999 ◽  
Vol 07 (04) ◽  
pp. 429-437 ◽  
Author(s):  
TERUYUKI WATANABE ◽  
JUNZO WATADA ◽  
KENJI ODA
Keyword(s):  
Mathematical Programming ◽  
Portfolio Selection ◽  
Real Life ◽  
Selection Problem ◽  
Boltzmann Machine ◽  
Strategic Investment ◽  
Portfolio Selection Problem ◽  
Multi Stage ◽  
Hierarchical Decision ◽  
Almost All

A conventional portfolio selection problem, which is based on a mean-variance model, is difficult to solve by using mathematical programming techniques. This difficulty is caused by the fact that the corresponding mathematical programming problems are large-dimensional one, since almost all variance-covariances of return rates are, typically, not zeros. In this paper, we propose an efficient method for solving a portfolio selection problem, a method which uses a Boltzmann machine. In a real-life problem, it is also important to find the optimal combination of a small number of invested securities out of many securities in a market, because of a limited amount of funds to invest into securities. So we also propose a portfolio selection method to obtain the invest ratio of limited number of securities out of huge number of securities using a multi-stage application of the Boltzmann machine.

A DOWNSIDE RISK APPROACH FOR THE PORTFOLIO SELECTION PROBLEM WITH FUZZY RETURNS

2004 ◽  
Vol 09 (01) ◽  
Author(s):  
Teresa León ◽  
Vicente Liern ◽  
Paulina Marco ◽  
Enriqueta Vercher ◽  
José Vicente Segura
Keyword(s):  
Portfolio Selection ◽  
Downside Risk ◽  
Selection Problem ◽  
Portfolio Selection Problem ◽  
Risk Approach
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