Document Type : Research Paper
Authors
1 School of Economics and Management, Beihang University, Beijing 100191, China
2 School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
3 Sinopec Management Institute, Beijing 100012, China
Abstract
In this paper, we consider portfolio selection problem in which
security returns are regarded as fuzzy variables rather than random variables.
We first introduce a concept of absolute deviation for fuzzy variables and
prove some useful properties, which imply that absolute deviation may be
used to measure risk well. Then we propose two mean-absolute deviation
models by defining risk as absolute deviation to search for optimal portfolios.
Furthermore, we design a hybrid intelligent algorithm by integrating genetic
algorithm and fuzzy simulation to solve the proposed models. Finally, we
illustrate this approach with two numerical examples.
Keywords
Multi-objective stochastic programming for portfolio selection},
Eur. J. Oper. Res., {\bf 177} (2007), 1811-1823.
{\it A fuzzy goal programming approach to portfolio selection}, Eur.
J. Oper. Res., {\bf 133} (2001), 287-297.
{\it Fuzzy compromise programming for portfolio selection}, Appl.
Math. Comput., {\bf 173} (2006), 251-264.
solutions to the quadratic mixed-integer mean-variance portfolio
selection problem}, Eur. J. Oper. Res., {\bf 176} (2007), 1947-1980.
%selection strategy with equilibrium}, Eur. J. Oper. Res., {\bf
%166}(2005), 278--292.
%downside risk: is there really that much difference?}, Eur. J. Oper.
%Res., {\bf 114}(1999), 304--319.
%portfolio selection}, Appl. Math. Comput., {\bf 177}(2006),
%500--507.
%fuzzy returns}, J. Intell. Fuzzy Syst., {\bf 18}(2007), 383--390.
for fuzzy protfolio selection}, J. Comput. Appl. Math., {\bf
217} (2008), 1-8.
deviation portfolio optimization model and its applications to Tokyo
Stock Market}, Manage. Sci., {\bf 37} (1991), 519-531.
measures}, Int. J. Uncertain. Fuzz., {\bf 14} (2006), 527-535.
principle for fuzzy variables}, Int. J. Uncertain. Fuzz., {\bf
15} (2007), 43-53.
model for portfolio selection with fuzzy returns}, Eur. J. Oper.
Res., {\bf 202} (2010), 239-247.
programming}, Physica-Verlag, Heidelberg, 2002.
Springer-Verlag, Berlin, 2007.
programming with fuzzy parameters}, Fuzzy Sets and Systems, {\bf
94} (1998), 227-237.
fuzzy expected value models}, IEEE T. Fuzzy Syst., {\bf 10} (2002),
445-450.
%mean-variance-skewness model for portfolio selection with
%transaction costs}, Int. J. Syst. Sci, {\bf 34}(2003), 255--262.
problems}, IEEE T. Fuzzy Syst., {\bf 14} (2006), 295-304.
diversification of investments}, Wiley, New York, 1959.
%mean-semivariance efficient sets by the critical line algorithm},
%Ann. Oper. Res., {\bf 45}(1993), 307--317.
fuzzy cross-entropy}, J. Comput. Appl. Math., {\bf 228} (2009),
139--149.
the mean vairance model versus the mean absolute deviation model},
Manage. Sci., {\bf 43} (1997), 1437-1446.
portfolio optimization}, Finance, {\bf 14} (1993), 107-123.
upper and lower exponential possibility distributions}, Eur. J.
Oper. Res., {\bf 114} (1999), 115-126.
fuzzy probabilities and possibility distributions}, Fuzzy Sets and
Systems, {\bf 111} (2000), 387-397.
portfolio optimization under downside risk measures}, Fuzzy Sets and
Systems, {\bf 158} (2007), 769-782.
problem on a single-line railway with fuzzy passenger demand}, IEEE
T. Fuzzy Syst., {\bf 17} (2009), 617-629.
problem and algorithm}, Appl. Soft Comput., {\bf 7} (2007), 879-889.
freight transportation planning with mixed uncertainty of randomness
and fuzziness}, Appl. Soft Comput., {\bf 11} (2011), 778-792.
portfolio selection problem}, Appl. Math. Comput., {\bf 159} (2004),
357-371.
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