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2016 | OriginalPaper | Buchkapitel

2. Credibilistic Mean-Variance-Skewness Model

verfasst von : Zhongfeng Qin

Erschienen in: Uncertain Portfolio Optimization

Verlag: Springer Singapore

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Abstract

Most of the existing works on portfolio optimization have been done based on only the first two moments of return distributions. However, there is a controversy over the issue of whether higher moments should be considered in portfolio selection.

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Vorheriges Kapitel Preliminaries

Nächstes Kapitel Credibilistic Mean-Absolute Deviation Model

Arditti FD (1967) Risk and the required return on equity. J Financ 22:19–36CrossRef

Arenas-Parra M, Bilbao-Terol A, Rodríguez-Uría M (2001) A fuzzy goal programming approach to portfolio selection. Eur J Oper Res 133:287–297CrossRef

Arnott RD, Wagner WH (1990) The measurement and control of trading costs. Financ Anal J 46(6):73–80CrossRef

Baule R (2010) Optimal portfolio selection for the small investor considering risk and transaction costs. OR Spectr 32:61–76CrossRef

Bawa VS (1975) Optimal rules for ordering uncertain prospects. J Financ Econ 2:95–121CrossRef

Bawa VS, Lindenberg EB (1977) Capital market equilibrium in a mean-lower partial moment framework. J Financ Econ 5:189–200CrossRef

Bertsimas D, Pachamanova D (2008) Robust multiperiod portfolio management in the presence of transaction costs. Comput Operat Res 35:3–17CrossRef

Bilbao-Terol A, Pérez-Gladish B, Arenas-Parra M, Rodrígez-Uría M (2006) Fuzzy compromise programming for portfolio selection. Appl Math Comput 173:252–264

Bitran GR (1980) Linear multiple objective problems with interval coefficients. Manag Sci 26:694–706CrossRef

Briec W, Kerstens K, Jokung O (2007) Mean-variance-skewness portfolio performance gauging: a general shortage function and dual approach. Manag Sci 53:135–149CrossRef

Cherny AS, Maslov VP (2003) On minimization and maximization of entropy in various disciplines. Theory Probab Appl 48:447–464CrossRef

Choi UJ, Jang B, Koo H (2007) An algorithm for optimal portfolio selection problem with transaction costs and random lifetimes. Appl Math Comput 191(1):239–252

de Andres-Sanchez J, Puchades LG (2012) Using fuzzy random variables in life annuities pricing. Fuzzy Sets Syst 188(1):27–44CrossRef

Fang SC, Rajasekera J, and Tsao H (1997) Entropy optimization and mathematical programming. Kluwer Academic, BostonCrossRef

Fang Y, Lai K, Wang S (2006) Portfolio rebalancing model with transaction costs based on fuzzy decision theory. Eur J Oper Res 175(2):879–893CrossRef

Glen JJ (2011) Mean-variance portfolio rebalancing with transaction costs and funding changes. J Oper Res Soc 62:667–676CrossRef

Grootveld H, Hallerbach W (1999) Variance vs downside risk: is there really that much difference? Eur J Oper Res 114:304–319CrossRef

Guo H, Wang X (2014) Variance of uncertain random variables. J Uncertain Anal Appl 2(6)

Gupta P, Mehlawat MK, Inuiguchi M, Chandra S (2014) Fuzzy portfolio optimization: advances in hybrid multi-criteria methodologies. Springer, BerlinCrossRef

Gupta P, Mehlawat MK, Saxena A (2008) Asset portfolio optimization using fuzzy mathematical programming. Inf Sci 178:1734–1755CrossRef

Gupta P, Mittal G, Mehlawat MK (2013) Expected value multiobjective portfolio rebalancing model with fuzzy paramters. Insur Math Econ 52:190–203CrossRef

Hao F, Liu Y (2009) Mean-variance models for portfolio selection with fuzzy random returns. J Appl Math Comput 30:9–38CrossRef

Harlow WV (1991) Asset allocation in a downside-risk framework. Financ Anal J 47(5):28–40CrossRef

Hasuike T, Katagiri H, Ishii H (2009) Portfolio selection problems with random fuzzy variable returns. Fuzzy Sets Syst 160:2579–2596CrossRef

Hirschberger M, Qi Y, Steuer R (2007) Randomly generating portfolio-selection covariance matrices with specified distributional characteristics. Eur J Oper Res 177:1610–1625CrossRef

Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

Huang T, Zhao R, Tang W (2009) Risk model with fuzzy random individual claim amount. Eur J Oper Res 192(3):879–890CrossRef

Huang X (2006) Fuzzy chance-constrained portfolio selection. Appl Math Comput 177(2):500–507

Huang X (2007a) Two new models for portfolio selection with stochastic returns taking fuzzy information. Eur J Oper Res 180:396–405CrossRef

Huang X (2007b) A new perspective for optimal portfolio selection with random fuzzy returns. Inf Sci 177:5404–5414CrossRef

Huang X (2008a) Mean-semivariance models for fuzzy protfolio selection. J Comput Appl Math 217:1–8CrossRef

Huang X (2008b) Mean-entropy models for fuzzy portfolio selection. IEEE Transact Fuzzy Syst 16(4):1096–1101CrossRef

Huang X (2010) Portfolio analysis: from probabilistic to credibilistic and uncertain approaches. Springer, BerlinCrossRef

Huang X (2012) A risk index model for portfolio selection with returns subject to experts’ estimations. Fuzzy Optim Decis Mak 11(4):451–463CrossRef

Huang X, Qiao L (2012) A risk index model for multi-period uncertain portfolio selection. Inf Sci 217:108–116CrossRef

Huang X, Ying H (2013) Risk index based models for portfolio adjusting problem with returns subject to experts’ evaluations. Econ Model 30:61–66CrossRef

Ida M (2003) Portfolio selection problem with interval coefficients. Appl Math Lett 16:709–713CrossRef

Kamdema JS, Deffo CT, Fono LA (2012) Moments and semi-moments for fuzzy portfolio selection. Insur Math Econ 51:517–530CrossRef

Kapur J, Kesavan H (1992) Entropy optimization principles with applications. Academic Press, New YorkCrossRef

Konno H, Koshizuka T (2005) Mean-absolute deviation model. IIE Trans 37:893–900CrossRef

Konno H, Shirakawa H, Yamazaki H (1993) A mean-absolute deviation-skewness portfolio optimization model. Ann Oper Res 45:205–220CrossRef

Konno H, Suzuki K (1995) A mean-variance-skewness optimization model. J Oper Res Soc Jpn 38:137–187

Konno H, Wijayanayake A (1999) Mean-absolute deviation portfolio optimization model under transaction costs. J Oper Res Soc Jpn 42(4):422–435CrossRef

Konno H, Yamazaki H (1991) Mean absolute portfolio optimisation model and its application to Tokyo stock market. Manag Sci 37(5):519–531CrossRef

Kraus A, Litzenberger R (1976) Skewness preference and the valuation of risky assets. J Financ 21:1085–1094

Kwakernaak H (1978) Fuzzy random variables. Inf Sci 15:1–29CrossRef

Lai KK, Wang S, Xu J, Zhu S, Fang Y (2002) A class of linear interval programming problems and its application to portfolio selection. IEEE Transact Fuzzy Syst 10:698–704CrossRef

Lai T (1991) Portfolio selection with skewness: a multiple-objective approach. Rev Quant Financ Acc 1:293–305CrossRef

Li J, Xu J (2007) A class of possibilistic portfolio selection model with interval coefficients and its application. Fuzzy Optim Decis Mak 6:123–137CrossRef

Li J, Xu J (2009) A novel portfolio selection model in a hybrid uncertain environment. Omega 37:439–449CrossRef

Li J, Xu J (2013) Multi-objective portfolio selection model with fuzzy random returns and a compromise approach-based genetic algorithm. Inf Sci 220:507–521CrossRef

Li P, Liu BD (2008) Entropy of credibility distributions for fuzzy variables. IEEE Transact Fuzzy Syst 16(1):123–129CrossRef

Li X (2015) Fuzzy cross-entropy. J Uncertain Anal Appl 3(2)

Li X, Liu BD (2006) A sufficient and necessary condition for credibility measures. Int J Uncertain Fuzziness Knowl-Based Syst 14(5):527–535CrossRef

Li X, Liu BD (2007) Maximum entropy principle for fuzzy variables. Int J Uncertain Fuzziness Knowl-Based Syst 15(2):43–52CrossRef

Li X, Qin Z (2014) Interval portfolio selection models within the framework of uncertainty theory. Econ Model 41:338–344CrossRef

Li X, Qin Z, Kar S (2010) Mean-variance-skewness model for portfolio selection with fuzzy parameters. Eur J Oper Res 202(1):239–247CrossRef

Li X, Shou B, Qin Z (2012) An expected regret minimization portfolio selection model. Eur J Oper Res 218(2):484–492CrossRef

Li X, Zhang Y, Wong H, Qin Z (2009) A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns. J Comput Appl Math 233:264–278CrossRef

Lin CC, Liu YT (2008) Genetic algorithms for portfolio selection problems with minimum transaction lots. Eur J Oper Res 185:393–404CrossRef

Liu BD (2002) Theory and practice of uncertain programming. Physica-Verlag, HeidelbergCrossRef

Liu BD (2004) Uncertainty theory. Springer, BerlinCrossRef

Liu BD (2007) Uncertainty theory, 2nd edn. Springer, Berlin

Liu BD (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinCrossRef

Liu BD, Iwamura K (1998) Chance constrained programming with fuzzy parameters. Fuzzy Sets Syst 94(2):227–237CrossRef

Liu BD, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10(4):445–450CrossRef

Liu SC, Wang S, Qiu W (2003) A mean-variance-skewness model for portfolio selection with transaction costs. Int J Syst Sci 34:255–262CrossRef

Liu YH, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186

Liu YH (2013a) Uncertain random variables: a mixture of uncertainty and randomness. Soft Comput 17(4):625–634CrossRef

Liu YH (2013b) Uncertain random programming with applications. Fuzzy Optim Decis Mak 12(2):153–169CrossRef

Liu YK (2006) Convergent results about the use of fuzzy simulation in fuzzy optimization problems. IEEE Transact Fuzzy Syst 14:295–304CrossRef

Liu YK, Gao JW (2007) The independence of fuzzy variables in credibility theory and its applications. Int J Uncertain Fuzziness Knowl-Based Syst 15(2):1–20CrossRef

Liu YK, Liu BD (2003) Expected value operator of random fuzzy variable and random fuzzy expected value models. Int J Uncertain Fuzziness Konwl-Based Syst 11:195–215CrossRef

Liu YK, Wu X, Hao F (2012) A new chance-variance optimization criterion for portfolio selection in uncertain decision systems. Expert Syst Appl 39:6514–6526CrossRef

Liu YX, Qin Z (2012) Mean semi-absolute deviation model for uncertain portfolio optimization problem. J Uncertain Syst 6(4):299–307

Lobo MS, Fazel M, Boyd S (2007) Portfolio optimization with linear and fixed transaction costs. Ann Oper Res 152:341–365CrossRef

Markowitz H (1952) Portfolio selection. J Financ 7:77–91

Markowitz H (1959) Portfolio selection: efficient diversification of investments. Wiley, New York

Markowitz H (1993) Computation of mean-semivariance efficient sets by the critical line algorithm. Ann Oper Res 45:307–317CrossRef

Morton AJ, Pliska SR (1995) Optimal portfolio management with transaction costs. Math Financ 5(4):337–356CrossRef

Ohlson JA, Ziemba WT (1976) Portfolio selection in a lognormal market when the investors has a power utility function. J Financ Quant Anal 11(1):57–71CrossRef

Papahristodoulou C, Dotzauer E (2004) Optimal portfolios using linear programming models. J Oper Res Soc 55:1169–1177CrossRef

Patel N, Subrahmanyam M (1982) A simple algorithm for optimal portfolio selection with fixed transaction costs. Manag Sci 28(3):303–314CrossRef

Peng ZX, Iwamura K (2010) A sufficient and necessary condition of uncertainty distribution. J Interdiscip Math 13(3):277–285CrossRef

Prakash AJ, Chang C, Pactwa TE (2003) Selecting a portfolio with skewness: recent evidence from US, European, and Latin American equity markets. J Bank Financ 27:1375–1390CrossRef

Price K, Price B, Nantell TJ (1982) Variance and lower partial moment measures of systematic risk: some analytical and empirical results. J Financ 37(3):843–855CrossRef

Qin Z (2015) Mean-variance model for portfolio optimzation problem in the simultaneous presence of random and uncertain returns. Eur J Oper Res 245:480–488CrossRef

Qin Z (2016) Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty. Appl Soft Comput. doi:10.1016/j.asoc.2016.06.017

Qin Z, Kar S (2013) Single-period inventory problem under uncertain environment. Appl Math Comput 219(18):9630–9638

Qin Z, Kar S, Li X (2009) Developments of mean-variance model for portfolio selection in uncertain environment. http://orsc.edu.cn/online/090511.pdf

Qin Z, Kar S, Zheng H (2016) Uncertain portfolio adjusting model using semiabsolute deviation. Soft Comput 20:717–725CrossRef

Qin Z, Li X, Ji X (2009) Portfolio selection based on fuzzy cross-entropy. J Comput Appl Math 228(1):139–149CrossRef

Qin Z, Wang ZD, Li X (2013) Mean-semivariance models for portfolio optimization with mixed uncertainty of fuzziness and randomness. Int J Uncertain Fuzziness Knowl-Based Syst 21(1):127–139CrossRef

Qin Z, Wen M, Gu C (2011) Mean-absolute deviation portfolio selection model with fuzzy returns. Iran J Fuzzy Syst 8(4):61–75

Qin Z, Xu L (2016) Mean-variance models for portfolio adjusting problem with fuzzy return returns. Technical report

Qin Z, Yao K (2014) Lower partial moments of uncertain variable and its application to portfolio selection. Technical report

Roy AD (1952) Safety first and the holding of assets. Econometrics 20:431–449CrossRef

Rubinstein R (2008) Semi-iterative minimum cross-entropy algorithms for rare-vents, counting, combinatorial and integer programming. Methodol Comput Appl Probab 10:121–178CrossRef

Sadati MEH, Nematian J (2013) Two-level linear programming for fuzzy random portfolio optimization through possibility and necessity-based model. Procedia Econ Financ 5:657–666CrossRef

Samuelson P (1970) The fundamental approximation theorem of portfolio analysis in terms of means, variances, and higher moments. Rev Econ Stud 37:537–542CrossRef

Shapiro A (2013) Modeling future lifetime as a fuzzy random variable. Insur Math Econ 53:864–870CrossRef

Shen Q, Zhao R (2010) Risk assessment of serious crime with fuzzy random theory. Inf Sci 180(22):4401–4411CrossRef

Sheng Y, Yao K (2014) Some formulas of variance of uncertain random variable. J Uncertain Anal Appl 2(12)

Simaan Y (1997) Estimation risk in portfolio selection: the mean vairance model versus the mean absolute deviation model. Manag Sci 43:1437–1446CrossRef

Simonelli MR (2005) Indeterminacy in portfolio selection. Eur J Oper Res 163:170–176CrossRef

Speranza MG (1993) Linear programming model for portfolio optimization. Finance 14:107–123

Steinbach MC (2001) Markowitz revisited: mean-variance models in financial portfolio analysis. SIAM Rev 43(1):31–85CrossRef

Tanaka H, Guo P (1999) Portfolio selection based on upper and lower exponential possibility distributions. Eur J Oper Res 114:115–126CrossRef

Tanaka H, Guo P, Türksen I (2000) Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets Syst 111:387–397CrossRef

Vercher E, Bermúdez J, Segura J (2007) Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets Syst 158:769–782CrossRef

Wang D, Qin Z, Kar S (2015) A novel single-period inventory problem with uncertain random demand and its application. Appl Math Comput 269:133–145

Woodside-Oriakhi M, Lucas C, Beasley JE (2013) Portfolio rebalancing with an investment horizon and transaction costs. Omega 41(2):406–420CrossRef

Wu M, Kong D, Xu J, Huang N (2013) On interval portfolio selection problem. Fuzzy Optim Decis Mak 12:289–304CrossRef

Yao K, Ji X (2014) Uncertain decision making and its application to portfolio selection problem. Int J Uncertain Fuzziness Knowl-Based Syst 22(1):113–123CrossRef

Yoshida Y (2009) An estimation model of value-at-risk portfolio under uncertainty. Fuzzy Sets Syst 160(22):3250–3262CrossRef

Yoshimoto A (1996) The mean-variance approach to portfolio optimization subject to transaction costs. J Oper Res Soc Jpn 39(1):99–117

Yu J, Lee W (2011) Portfolio rebalancing model using multiple criteria. Eur J Oper Res 209(2):166–175CrossRef

Yu M, Takahashi S, Inoue H, Wang S (2010) Dynamic portfolio optimization with risk control for absolute deviation model. Eur J Oper Res 201(2):349–364CrossRef

Yu L, Wang S, Lai KK (2008) Neural network-based mean-variance-skewness model for portfolio selection. Comput Oper Res 35(1):34–46CrossRef

Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28CrossRef

Zhang P, Zhang W (2014) Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints. Fuzzy Sets Syst 255(16):74–91CrossRef

Zhang W, Wang Y, Chen Z, Nie Z (2007) Possibilisitc mean-variance models and efficient frontiers for portfolio selection problem. Inf Sci 177:2787–2801CrossRef

Zhang W, Zhang X, Chen Y (2011) Portfolio adjusting optimization with added assets and transaction costs based on credibility measures. Insur Math Econ 49(3):353–360CrossRef

Zhang X, Zhang W, Cai R (2010) Portfolio adjusting optimization under credibility measures. J Comput Appl Math 234(5):1458–1465CrossRef

Zhu S, Li D, Wang S (2009) Robust portfolio selection under downside risk measures. Quantit Financ 9(7):869–885CrossRef

Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst 41(7):535–547CrossRef

Ziemba WT, Parkan C, Brooks-Hill R (1974) Calculation of investment portfolios with risk free borrowing and lending. Manag Sci 21(2):209–222CrossRef

Titel: Credibilistic Mean-Variance-Skewness Model
verfasst von: Zhongfeng Qin
Verlag: Springer Singapore
Buch: Uncertain Portfolio Optimization
Print ISBN: 978-981-10-1809-1

Electronic ISBN: 978-981-10-1810-7

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-981-10-1810-7_2