A Dynamic Average Value-at-Risk Portfolio Model with Fuzzy Random Variables

• Published in: Fuzzy Sets, Rough Sets, Multisets and Clustering Vol. 671; pp. 291 - 306
• Main Author: Yoshida, Yuji
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2017; Springer International Publishing
• Series: Studies in Computational Intelligence
• Subjects: Artificial intelligence; Asset Price; Evaluation Weight; Fuzzy Number; Optimal Portfolio; Risk Probability
• DOI: 10.1007/978-3-319-47557-8_17
• ISBN: 3319475568; 9783319475561
• ISSN: 1860-949X

A perception-based portfolio model under uncertainty is presented. In the proposed model, randomness and fuzziness are evaluated respectively by probabilistic expectation and the mean values with evaluation weights and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}-mean functions. Introducing average value-at-risks under conditions, this paper formulates average value-at-risks in dynamic stochastic environment. By dynamic programming approach, an optimality condition of the optimal portfolios for dynamic average value-at-risks is derived. It is shown that the optimal average value-at-risk is a solution of the optimality equation under a reasonable assumption, and an optimal portfolio weight is obtained from the equation.