Abstract
Inspired by Li (2019) who considers one parameter, we propose a novel two-parameter coherent fuzzy number (TPCFN) that can flexibly capture investors’ attitudes (pessimistic, optimistic, or neutral). We define the possibilistic density function, the possibilistic distribution function, the possibilistic mean, and the possibilistic variance of the TPCFN for the first time. Furthermore, we derive the above statistical characteristics with numerical expressions through rigorous mathematical proof. The monotonicity of the possibilistic mean and possibilistic variance are presented by the first-order derivative and illustrated with figures in detail. In addition, we discuss the investors’ attitudes by using different parameter values and their influences on the mean and variance. Then, we construct an equal-weighted model, a mean–variance model, and a regret minimization model with TPCFN, respectively. We carry out a sensitivity analysis to explore the parametric influence on the model’s solution. At the same time, we compare different models with the same parameter values. Finally, we use a numerical example to demonstrate the feasibility and effectiveness of our proposed models. We compare the performance of the three models by five indexes (annual return, Sharpe ratio, beta value, unsystematic risk, and alpha value). The results show that optimistic investors can obtain more gains in the three models. Our minimization model considering the regret factor outperforms the mean–variance model and the equal-weighted portfolio in returns when the parameter values are the same.
Similar content being viewed by others
Availability of data and materials
The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.
References
Adcock C (2014) Mean-variance-skewness efficient surfaces, stein’s lemma and the multivariate extended skew-student distribution. Eur J Oper Res 234(2):392–401
Arrsoy Y E, Bali T G (2018) Regret in financial decision making under volatility uncertainty. Georgetown McDonough School of Business Research Paper 3195191
Baule R, Korn O, Kuntz LC (2019) Markowitz with regret. J Econ Dyn Control 103:1–24
Bell DE (1982) Regret in decision making under uncertainty. Oper Res 30(5):961–981
Carlsson C, Fuller R (2001) On possibilistic mean value and variances of fuzzy numbers. Turku Centre Comput Sci 122(2):315–326
Chorus CG, Arentze TA, Timmermans HJP (2008) A random regret minimization model of travel choice. Transp Res Part B 42(1):1–18
Chorus CG (2010) A new model of random regret minimization. Eur J Transp Infrastruct Res 10(2):181–196
Dubois D, Prade H (1983) Ranking of fuzzy numbers in the setting of possibilistic theory. Inf Sci 30:183–224
Fioretti M, Vostroknutov A, Coricelli G (2022) Dynamic regret avoidance. Am Econ J Microecon 14(1):70–93
Frydman C, Camerer C (2016) Neural evidence of regret and its implications for investor behavior. Soc Sci Electron Pub 29(11):3108–3139
Gong X, Min L, Yu C (2022) Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels. Appl Soft Comput 114:108104
Gong X, Yu C, Min L, Ge Z (2021) Regret theory-based fuzzy multi-objective portfolio selection model involving DEA cross-efficiency and higher moments. Appl Soft Comput 100:106958
Gupta P, Mehlawat MK, Yadav S, Kumar A (2020) Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio opti-mization models. Soft Comput 24(16):11931–11956. https://doi.org/10.1007/s00500-019-04639-3
Herweg F, Müller D (2021) A comparison of regret theory and salience theory for decisions under risk. J Econ Theory 193:105226. https://doi.org/10.1016/j.jet.2021.105226
Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manage Sci 37(5):519–531
Lai ZR, Li C, Wu XT, Guan QL, Fang LD (2022) Multi trend conditional value at risk for portfolio optimization. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3183891
Li HQ, Yi ZH (2019) Portfolio selection with coherent Investor’s expectations under uncertainty. Expert Syst Appl 133:49–58. https://doi.org/10.1016/j.eswa.2019.05.008
Li MT, Xu QF, Jiang CX, Zhao QN (2023) The role of tail network topological characteristic in portfolio selection: a TNA-PMC model. Int Rev Financ 23(1):37–57. https://doi.org/10.1111/irfi.12379
Li X, Guo S, Yu L (2015) Skewness of fuzzy numbers and its applications in portfolio selection. IEEE Trans Fuzzy Syst 23:2135–2143
Li X, Qin Z, Kar S (2010) Mean-variance-skewness model for portfolio selection with fuzzy returns. Eur J Oper Res 202(1):239–247
Li X, Shou B, Qin Z (2012) An expected regret minimization portfolio selection model. Eur J Oper Res 218(2):484–492. https://doi.org/10.1016/j.ejor.2011.11.015
Loomes GSR (2015) Regret theory: an alternative theory of rational choice under uncertainty. Econ J 125(583):512–532
Magron C, Merli M (2015) Repurchase behavior of Individual Investors, Sophistication and Regret. J Bank Finance 61:15–26
Mao JCT (1970) Models of capital budgeting, E-V VS E-S. J Financ Quant Anal 4(5):657–675
Markowitz HM (1952) Portfolio selection. J Finance 7(1):77–91
Mehlawat MK, Kumar A, Yadav S, Chen W (2018) Data envelopment analysis based fuzzy multi-objective portfolio selection model involving higher moments. Inf Sci 460:128–150
Mehlawat MK, Gupta P, Khan AZ (2021) Multiobjective portfolio optimization using coherent fuzzy numbers in a credibilistic environment. Int J Intell Syst 36(4):1560–1594. https://doi.org/10.1002/int.22352
Ouzan S (2020) Loss aversion and market crashes. Econ Model 1171 92:70–86. https://doi.org/10.1016/j.econmod.2020.06.015
Pankaj G, Mukesh KM, Ahmad ZK (2021) Multi-period portfolio optimization using coherent fuzzy numbers in a credibilistic environment. Expert Syst Appl 176:114135
Qin J (2020) Regret based capital asset pricing model. J Bank Finance 114:105784
Samuelson P (1958) The fundamental approximation theorem of portfolio analysis in terms of means variances and higher moments. Rev Econ Stud 25:65–68
Speranza MG (1993) Linear programming models for portfolio optimization. J Finance 14:107–123
Tong X, Qi L, Wu F, Zhou H (2010) A smoothing method for solving portfolio optimization with CVaR and applications in allocation of generation asset. Appl Math Comput 216(6):1723–1740
Vercher E, Bermudez JD (2013) A possibilistic mean-downside risk-skewness model for efficient portfolio selection. IEEE Trans Fuzzy Syst 21:585–595
Xidonas P, Mavrotas G, Hassapis C (2017) Robust multiobjective portfolio optimization: a minimax regret approach. Eur J Oper Res 262(1):299–305
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibilistic. Fuzzy Sets Syst 1(1):3–28. https://doi.org/10.1016/0165-0114(78)90029-5
Acknowledgements
This research was supported by “the National Social Science Foundation Projects of China, No. 21BTJ069”. The authors are highly grateful to the referees and editor in-chief for their very helpful advice and comments.
Funding
This research was supported by “the National Social Science Foundation Projects of China, No. 21BTJ069”.
Author information
Authors and Affiliations
Contributions
XD (First Author): Conceptualization, Software Investigation, Formal Analysis, Methodology and Funding Acquisition; FG (Corresponding Author): Data Curation, Writing Original Draft, Validation, Supervision, Writing Review and Editing.
Corresponding author
Ethics declarations
Conflict of interest
We declare that we have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Deng, X., Geng, F. Portfolio model with a novel two-parameter coherent fuzzy number based on regret theory. Soft Comput 27, 17189–17212 (2023). https://doi.org/10.1007/s00500-023-08978-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-023-08978-0