Portfolios optimization with coherent risk measures in fuzzy asset management

An portfolio optimization problem with fuzzy random variables is discussed. Risk measures for fuzzy random variables are introduced by perception-based approach. Randomness is estimated stochastically, and fuzziness are evaluated by the mean values with evaluation weights and λ-mean functions. Using coherent risk measures, we discuss a portfolio optimization problem under randomness and fuzziness. By analytical approach, we derive a solution of the portfolio problem. A numerical example is given to explain the results.