Abstract
In a world under uncertainty, the beliefs for the information underlie the behavioral style of portfolio decisions in portfolio management. In this work, we use the copula-based ordered modular averages (OMAs) in the calculation of the mean and variance of the assets’ returns for portfolio selection to capture the beliefs of the investors and the departure of rationality in evaluation. Specially, the outcomes and the probability information in terms of the decumulative probabilities are jointly transformed using appropriate copulas while satisfying the stochastic dominance in the probability-sensitivity evaluation. In addition, the diversity of the underlying copulas facilitates the challenge of the diversity of investors with different beliefs for expectations. Consequently, the mean-variance model in this work using OMA with the decumulative probabilities can encode not only the decision makers’ assessment of relative likelihoods but also the confidence attached to such assessment in the evaluation.
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The data is extracted from WIND (www.wind.com.cn).
References
Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation functions: A guide for practitioners (Vol. 221). Heidelberg: Springer.
Fang, Y., Lai, K. K., & Wang, S. (2008). Fuzzy portfolio optimization: Theory and methods (Vol. 609). Berlin: Springer.
Huang, X. (2008). Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics, 217(1), 1–8.
Huang, X. (2009). A review of credibilistic portfolio selection. Fuzzy Optimization and Decision Making, 8(3), 263–281.
Klement, E. P., Mesiar, R., & Pap, E. (2000). Triangular norms (Vol. 8). Kluwer Academic Publishers.
Klement, E. P., Mesiar, R., & Pap, E. (2004). Measure-based aggregation operators. Fuzzy Sets and Systems, 142(1), 3–14.
Laengle, S., Loyola, G., & Merigo, J. (2016). Mean-variance portfolio selection with the ordered weighted average. IEEE Transactions on Fuzzy Systems, 25(2), 350–360.
Liu, B. (2002). Theory and practice of uncertain programming. Berlin: Springer.
Lopes, L. L., & Oden, G. C. (1999). The role of aspiration level in risky choice: A comparison of cumulative prospect theory and SP/A theory. Journal of Mathematical Psychology, 43(2), 286–313.
Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.
Merigó, J. M., Guillén, M., & Sarabia, J. M. (2015). The ordered weighted average in the variance and the covariance. International Journal of Intelligent Systems, 30(9), 985–1005.
Mesiar, R., & Mesiarova-Zemankova, A. (2011). The ordered modular averages. IEEE Transactions on Fuzzy Systems, 19(1), 42–50.
Nelsen, R. B. (2007). An introduction to copulas. Springer.
Quiggin, J. (2014). Non-expected utility models under objective uncertainty. In Handbook of the economics of risk and uncertainty (Vol. 1, pp. 701–728). Elsevier.
Quiggin, J. (1982). A theory of anticipated utility. Journal of Economic Behavior & Organization, 3(4), 323–343.
Schmeidler, D. (1989). Subjective probability and expected utility without additivity. Econometrica, 57(3), 571–587.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.
Wakker, P. P. (2010). Prospect theory: For risk and ambiguity. New York: Cambridge University Press.
Wang, S., & Xia, Y. (2012). Portfolio selection and asset pricing (Vol. 514). Springer.
Wang, S., & Zhu, S. (2002). On fuzzy portfolio selection problems. Fuzzy Optimization and Decision Making, 1(4), 361–377.
Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183–190.
Yager, R. R. (1993). Families of OWA operators. Fuzzy Sets and Systems, 59(2), 125–148.
Yager, R. R. (1998). Including importances in OWA aggregations using fuzzy systems modeling. IEEE Transactions on Fuzzy Systems, 6(2), 286–294.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
Acknowledgements
We are grateful to Committee of the 3rd International Symposium on Interval Data Modelling (SIDM2017, Beijing) co-chaired by Prof. Shouyang Wang and Prof. Yongmiao Hong for the opportunity to present the topic and specially the helpful comments and suggestions by the participants (However, the authors are responsible for all of the possible errors.). Special thanks go to the editors and the referees for their careful work and valuable comments on the improvement of manuscript.
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The work is supported by National Natural Science Foundation of China under Grants 71473081 and 71871092, and Hunan Provincial Innovation Foundation For Postgraduate Grant CX2017B171.
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Li, HQ., Yi, ZH. & Fang, Y. Portfolio selection under uncertainty by the ordered modular average operator. Fuzzy Optim Decis Making 18, 1–14 (2019). https://doi.org/10.1007/s10700-018-9295-2
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DOI: https://doi.org/10.1007/s10700-018-9295-2