An Average Value-at-Risk Portfolio under Uncertainty

Yuji Yoshida

An average value-at-risk portfolio model under randomness and fuzziness is discussed. The randomness and fuzziness are evaluated respectively by the probabilistic expectation and the mean with evaluation weights and lambda-mean functions. Extending the average value-at-risk, this paper formulates an average value-at-risk portfolio problem with fuzzy random variables. The analytical solutions of the average value-at-risk portfolio problem are derived. A numerical example is given to explain our idea.

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