JACIII Vol.15 No.1 pp. 56-62
doi: 10.20965/jaciii.2011.p0056


Risk Analysis of Portfolios Under Uncertainty: Minimizing Average Rates of Falling

Yuji Yoshida

Faculty of Economics and Business Administration, University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu 802-8577, Japan

February 12, 2010
April 22, 2010
January 20, 2011
average value-at-risk, risk-sensitive portfolio, fuzzy random variable, perception-based extension, probability of bankruptcy

A portfolio model to minimize the risk of falling under uncertainty is discussed. The risk of falling is represented by the value-at-risk of rate of return. Introducing the perception-based extension of the average value-at-risk, this paper formulates a portfolio problem to minimize the risk of falling with fuzzy random variables. In the proposed model, randomness and fuzziness are evaluated respectively by the probabilistic expectation and the mean with evaluation weights and λ-mean functions. The analytical solutions of the portfolio problem regarding the risk of falling are given. This paper gives formulae to show the explicit relations among the following important parameters in portfolio: the expected rate of return, the risk probability of falling and bankruptcy, and the average rate of falling regarding the asset prices. A numerical example is given to explain how to obtain the optimal portfolio and these parameters from the asset prices in the stock market.

Cite this article as:
Yuji Yoshida, “Risk Analysis of Portfolios Under Uncertainty: Minimizing Average Rates of Falling,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.1, pp. 56-62, 2011.
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