Skip to main content
SpringerLink
Log in

Portfolio model with a novel two-parameter coherent fuzzy number based on regret theory

  • Soft computing in decision making and in modeling in economics
  • Published:
Soft Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Bell DE (1982) Regret in decision making under uncertainty. Oper Res 30(5):961–981

    Article  MATH  Google Scholar 

  • Carlsson C, Fuller R (2001) On possibilistic mean value and variances of fuzzy numbers. Turku Centre Comput Sci 122(2):315–326

    MathSciNet  MATH  Google Scholar 

  • Chorus CG, Arentze TA, Timmermans HJP (2008) A random regret minimization model of travel choice. Transp Res Part B 42(1):1–18

    Article  Google Scholar 

  • Chorus CG (2010) A new model of random regret minimization. Eur J Transp Infrastruct Res 10(2):181–196

    Google Scholar 

  • Dubois D, Prade H (1983) Ranking of fuzzy numbers in the setting of possibilistic theory. Inf Sci 30:183–224

    Article  MATH  Google Scholar 

  • Fioretti M, Vostroknutov A, Coricelli G (2022) Dynamic regret avoidance. Am Econ J Microecon 14(1):70–93

    Article  Google Scholar 

  • Frydman C, Camerer C (2016) Neural evidence of regret and its implications for investor behavior. Soc Sci Electron Pub 29(11):3108–3139

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manage Sci 37(5):519–531

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Li X, Guo S, Yu L (2015) Skewness of fuzzy numbers and its applications in portfolio selection. IEEE Trans Fuzzy Syst 23:2135–2143

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Loomes GSR (2015) Regret theory: an alternative theory of rational choice under uncertainty. Econ J 125(583):512–532

    Google Scholar 

  • Magron C, Merli M (2015) Repurchase behavior of Individual Investors, Sophistication and Regret. J Bank Finance 61:15–26

    Article  Google Scholar 

  • Mao JCT (1970) Models of capital budgeting, E-V VS E-S. J Financ Quant Anal 4(5):657–675

    Article  Google Scholar 

  • Markowitz HM (1952) Portfolio selection. J Finance 7(1):77–91

    Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Ouzan S (2020) Loss aversion and market crashes. Econ Model 1171 92:70–86. https://doi.org/10.1016/j.econmod.2020.06.015

    Article  Google Scholar 

  • Pankaj G, Mukesh KM, Ahmad ZK (2021) Multi-period portfolio optimization using coherent fuzzy numbers in a credibilistic environment. Expert Syst Appl 176:114135

    Google Scholar 

  • Qin J (2020) Regret based capital asset pricing model. J Bank Finance 114:105784

    Article  Google Scholar 

  • Samuelson P (1958) The fundamental approximation theorem of portfolio analysis in terms of means variances and higher moments. Rev Econ Stud 25:65–68

    Google Scholar 

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

    Google Scholar 

  • 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

    MathSciNet  MATH  Google Scholar 

  • Vercher E, Bermudez JD (2013) A possibilistic mean-downside risk-skewness model for efficient portfolio selection. IEEE Trans Fuzzy Syst 21:585–595

    Article  Google Scholar 

  • Xidonas P, Mavrotas G, Hassapis C (2017) Robust multiobjective portfolio optimization: a minimax regret approach. Eur J Oper Res 262(1):299–305

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

Download references

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

Author notes

  1. Fengting Geng

    Present address: School of Mathematics, South China University of Technology, Guangzhou, 510640, China

Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Xue Deng

Authors
  1. Xue Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fengting Geng
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Correspondence to Fengting Geng.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-08978-0

Keywords

Search

Navigation