Abstract
This paper discusses a risk-sensitive portfolio problem, where the objective function is defined by randomness and fuzziness, and it introduces the perception-based extension of the expectation and the variance for fuzzy random variables. Fuzzy random variables are estimated by mean and variance with λ-mean functions and evaluation weights: A possibility-necessity weight ν for subjective estimation, and a pessimistic-optimistic index λ for subjective decision. A solution of the risk-sensitive portfolio problem is derived by quadratic programming approach.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Carlsson, C., Fullér, R.: On Possibilistic Mean Value and Variance of Fuzzy Numbers. Fuzzy Sets and Systems, pp. 315–326 (2001)
Feng, Y., Hu, L., Su, H.: The Variance and Covariance of Fuzzy Random Variables. Fuzzy Sets and Systems, pp. 487–497 (2001)
Fortemps, P., Roubens, M.: Ranking and Defuzzification Methods Based on Area Compensation. Fuzzy Sets and Systems, pp. 319–330 (1996)
Kruse, R., Meyer, K.D.: Statistics with Vague Data. Riedel Publ. Co., Dortrecht (1987)
Inuiguchi, M., Tanino, T.: Portfolio Selection under Independent Possibilistic Information. Fuzzy Sets and Systems, pp. 83–92 (2000)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, London (1995)
Kwakernaak, H.: Fuzzy Random Variables – I. Definitions and Theorem. Inform. Sci., 1–29 (1978)
Markowits, H.: Mean-Variance Analysis in Portfolio Choice and Capital Markets. Blackwell Publ., Oxford (1990)
Pliska, S.R.: Introduction to Mathematical Finance: Discrete-Time Models. Blackwell Publ., New York (1997)
Puri, M.L., Ralescu, D.A.: Fuzzy Random Variables. J. Math. Anal. Appl. 114, 409–422 (1986)
Yoshida, Y.: A Mean Estimation of Fuzzy Numbers by Evaluation Measures. In: Negoita, M.G., Howlett, R.J., Jain, L.C. (eds.) KES 2004. LNCS (LNAI), vol. 3214, pp. 1222–1229. Springer, Heidelberg (2004)
Yoshida, Y.: Mean values, Measurement of Fuzziness and Variance of Fuzzy Random Variables for Fuzzy Optimization. In: Proc. SCIS & ISIS, pp. 2277–2282 (2006)
Yoshida, Y.: Fuzzy Extension of Estimations with Randomness: The Perception-based Approach. In: Torra, V., Narukawa, Y., Yoshida, Y. (eds.) MDAI 2007. LNCS (LNAI), vol. 4617, pp. 295–306. Springer, Heidelberg (2007)
Zadeh, L.A.: Fuzzy Sets. Inform. and Control, 338–353 (1965)
Zadeh, L.A.: Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities. J. Stat. Plan. Infer., 233–264 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yoshida, Y. (2008). A Risk-Sensitive Portfolio with Mean and Variance of Fuzzy Random Variables. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2008. Lecture Notes in Computer Science(), vol 5227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85984-0_44
Download citation
DOI: https://doi.org/10.1007/978-3-540-85984-0_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85983-3
Online ISBN: 978-3-540-85984-0
eBook Packages: Computer ScienceComputer Science (R0)