MULTIPERIOD CREDIBILITIC MEAN SEMI-ABSOLUTE DEVIATION PORTFOLIO SELECTION

Document Type: Research Paper

Author

School of Economics and Management, South China Normal University, Guangzhou 510006, P. R. China

Abstract

In this paper, we discuss a multiperiod portfolio selection problem with fuzzy returns. We present a new credibilitic multiperiod mean semi- absolute deviation portfolio selection with some real factors including transaction costs, borrowing constraints, entropy constraints, threshold constraints and risk control. In the proposed model, we quantify the investment return and risk associated with the return rate on a risky asset by its credibilitic expected value and semi- absolute deviation. Since the proposed model is a nonlinear dynamic optimization problem with path dependence, we design a novel forward dynamic programming method to solve it. Finally, we provide a numerical example to demonstrate the performance of the designed algorithm and the application of the proposed model.

Keywords


[1] T. Bodnar, N. Parolya and W. Schmid, A closed-form solution of the multi-period portfo-
lio choice problem for a quadratic utility function, Annals of Operations Research, 229(1)
(2015), 121{158.
[2] K. C. Butler and D. C. Joaquin, Are the gains from international portfolio diversi fication
exaggerated? The in
fluence of downside risk in bear markets, Journal of International Money
and Finance, 21(7) (2002), 981{1011.
[3] G. C. Cala ore, Multi-period portfolio optimization with linear control policies, Automatica,
44(10) (2008), 2463{2473.
[4] U. C elikyurt and S.  Oekici, Multiperiod portfolio optimization models in stochastic mar-
kets using the meanCvariance approach, European Journal of Operational Research, 179(1)
(2007), 186{202.
[5] J. Estrada, The cost of equity in Internet stocks: a downside risk approach, European J.
Finance, 10(4) (2004), 239{254.
[6] Y. Fang, K. K. Lai and S. Y. Wang, Portfolio rebalancing model with transaction costs based
on fuzzy decision theory, European Journal of Operational Research, 175(2) (2006), 879{893.
[7] N. Gulpnar and B. Rustem, Worst-case robust decisions for multi-period meanCvariance
portfolio optimization, European Journal of Operational Research, 183(3) (2007), 981{1000.
[8] X. Huang, Mean-semivariance models for fuzzy portfolio selection, Journal of Computational
and Applied Mathematics, 217(1) (2008), 1-8.
[9] X. Huang and L. Qiao, A risk index model for multi-period uncertain portfolio selection,
Information Sciences, 217(24) (2012), 108{116.
[10] J. E. Ingersoll, Theory of Financial Decision Making, Rowman & Little eld, Savage, (1987),
82{92.
[11] P. Jana, T. K. Roy and S. K. Mazumder, Multi-objective possibilistic model for portfolio
selection with transaction cost, Journal of Computational and Applied Mathematics, 228(1)
(2009), 188{196.
[12] J. N. Kapur, Maximum Entropy Models in Science and Engineering, Wiley Eastern Limited,
New Delhi, (1990), 428{436.

[13] M. Koksalan and C. T. Sakar, An interactive approach to stochastic programming-based
portfolio optimization, To appear in Annals of Operations Research, 245(1{2) (2016), 47{
66.
[14] H. Konno and H. Yamazaki, Mean absolute portfolio optimisation model and its application
to Tokyo stock market, Management Science ,37(5) (1991), 519{531.
[15] C. J. Li and Z. F. Li, Multi-period portfolio optimization for assetCliability management with
bankrupt control, Applied Mathematics and Computation, 218(22) (2012), 11196{11208.
[16] D. Li and W. L. Ng, Optimal dynamic portfolio selection: multiperiod meanCvariance for-
mulation, Mathematical Finance, 10(3) (2000), 387{406.
[17] X. Li, Z. Qin and S. Kar, Mean-variance-skewness model for portfolio selection with fuzzy
returns, European Journal of operational Research, 202(1)(2010), 239{247.
[18] D. Lien and Y. K. Tse, Hedging downside risk: futures vs options, Internat. Rev. Econom.
Finance, 10(2) (2001), 159{169.
[19] B. Liu, Inequalities and convergence concepts of fuzzy and rough variables, Fuzzy Optimization
and Decision Making, 2 (2) (2003), 87{100.
[20] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE
Transactions on Fuzzy Systems, 10(4) (2002), 445{450.
[21] Y. J. Liu and W. G. Zhang, A multi-period fuzzy portfolio optimization model with minimum
transaction lots, European Journal of Operational Research, 242 (3) (2015), 933{941 .
[22] Y.J. Liu, W. G. Zhang and Q. Zhang, Credibilistic multi-period portfolio optimization model
with bankruptcy control and affine recourse, Applied Soft Computing, 38(3) (2016), 890{906.
[23] R. Mansini, W. Ogryczak and M. G. Speranza, Conditional value at risk and related lin-
ear programming models for portfolio optimization, Annals of Operations Research ,152(1)
(2007), 227{256.
[24] H. M. Markowitz, Portfolio selection, Journal of Finance, 7(1) (1952),77{91.
[25] Y. Simaan, Estimation risk in portfolio selection: The mean variance model and the mean-
absolute deviation model, Management Science, 43(10) (1997), 1437{1446.
[26] M.G. Speranza, Linear programming model for portfolio optimization, Finance, 14(1) (1993),
107{123.
[27] S. Stevenson, Emerging markets, downside risk and the asset allocation decision, Emerging
Markets Rev., 2(1) (2001), 50{66.
[28] A. B. Terol, B. P. Gladish, M. A. Parra and M. V. R. Ura, Fuzzy compromise programming
for portfolio selection, Applied Mathematics and Computation, 173(1) (2006), 251{264
[29] J. H. Van Binsbergen and M. Brandt, Solving dynamic portfolio choice problems by recursing
on optimized portfolio weights or on the value function?, Computational Economics ,29(3-4)
(2007), 355{367.
[30] E. Vercher, J. Bermudez and J. Segura, Fuzzy portfolio optimization under downside risk
measures, Fuzzy Sets and Systems, 158(7) (2007), 769{782.
[31] S.Y. Wang and S.S. Zhu, On fuzzy portfolio selection problem, Fuzzy Optimization and
Decision Making, 1(14) (2002),361{377
[32] H. L. Wu and Z. F. Li, Multi-period meanCvariance portfolio selection with regime switching
and a stochastic cash
ow, Insurance: Mathematics and Economics, 50(3) (2012), 371{384.
[33] W. Yan and S. R. Li, A class of multi-period semi-variance portfolio selection with a four-
factor futures price model, Journal of Applied Mathematics and Computing, 29(1-2) (2009),
19{34.
[34] W. Yan, R. Miao and S.R. Li, Multi-period semi-variance portfolio selection: Model and
numerical solution, Applied Mathematics and Computation, 194(1)(2007), 128{134
[35] M. Yu, S. Takahashi, H. Inoue and S. Y. Wang, Dynamic portfolio optimization with risk
control for absolute deviation model, European Journal of Operational Research, 201(2)
(2010), 349{364.
[36] M. Yu and S. Y. Wang, Dynamic optimal portfolio with maximum absolute deviation model,
Journal of Global Optimization, 53(2) (2012), 363{380.
[37] L. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1(3-28)
(1978), 61{72.

[38] L. Zadeh, A theory of approximate reasoning, in: J. Hayes, D. Michie, R.M. Thrall (Eds.),
Mathematical Frontiers of the Social and Policy Sciences, Westview Press, Boulder, Colorado,
(1979), 69{129.
[39] W. G. Zhang, Y. J. Liu and W. J. Xu, A new fuzzy programming approach for multi-period
portfolio Optimization with return demand and risk control, Fuzzy Sets and Systems, 246(4)
(2014), 107{126.
[40] W. G. Zhang and Y. J. Liu, Credibilitic mean-variance model for multi-period portfolio se-
lection problem with risk control, OR Spectrum, 36(1) (2014), 113{132.
[41] W.G. Zhang, Y. J. Liu and W. J. Xu, A possibilistic mean-semivariance-entropy model
for multi-period portfolio selection with transaction costs, European Journal of Operational
Research, 222(2) (2012), 341{349.
[42] W. G. Zhang, Y. L. Wang, Z. P. Chen and Z. K. Nie, Possibilistic meanCvariance models
and ecient frontiers for portfolio selection problem, Information Sciences, 177(13) (2007),
2787{2801.
[43] P. Zhang and W. G. Zhang, Multiperiod mean absolute deviation fuzzy portfolio selection
model with risk control and cardinality constraints, Fuzzy Sets and Systems, 255(2) (2014),
74{91.
[44] W. G. Zhang, X. L. Zhang and W. L. Xiao, Portfolio selection under possibilistic meanC-
variance utility and a SMO algorithm, European Journal of Operational Research, 197(2)
(2009), 693{700.
[45] S. S. Zhu, D. Li and S. Y. Wang, Risk control over bankruptcy in dynamic portfolio selection:
a generalized meanCvariance formulation, IEEE Transactions on Automatic Control, 49(3)
(2004), 447{457.