Portfolio optimization in fuzzy asset management with coherent risk measures derived from risk averse utility

A portfolio optimization problem with fuzzy random variables is discussed using coherent risk measures, which are characterized by weighted average value-at-risks with risk spectra. By perception-based approach, coherent risk measures and weighted average value-at-risks are extended for fuzzy random variables. Coherent risk measures derived from risk averse utility functions are introduced to discuss the portfolio optimization with randomness and fuzziness. The randomness is estimated by probability, and the fuzziness is evaluated by lambda-mean functions and evaluation weights. By mathematical programming approaches, a solution is derived for the risk-minimizing portfolio optimization problem. Numerical examples are given to compare coherent risk measures. It is made clear that coherent risk measures derived from risk averse utility functions have excellent properties as risk criteria for these optimization problems. Not only pessimistic and necessity case but also optimistic and possibility case are calculated numerically to deal with uncertain information.