nach oben

Erschienen in:

2016 | OriginalPaper | Buchkapitel

6. Uncertain Mean-LPMs Model

verfasst von : Zhongfeng Qin

Erschienen in: Uncertain Portfolio Optimization

Verlag: Springer Singapore

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Downside risk is a class of risk measures which focuses on the asymmetry of returns about some target level of return (Harlow 1991). It has gradually attracted more and more attentions since investors are often sensitive to downside losses, relative to upside gains. Moreover, it requires simpler theoretical assumptions to justify its application. In portfolio management, investors always prefer securities with smaller downside risk. In the situation with symmetrically distributed returns, some downside risks are consistent with general risk measures. For example, semivariance is exactly proportional to variance for normal distribution, which implies they are equivalent in measuring risk.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Uncertain Mean-Semiabsolute Deviation Model

Nächstes Kapitel Interval Mean-Semiabsolute 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: Uncertain Mean-LPMs 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_6