Portfolio optimization with perception-based risk measures in dynamic fuzzy asset management

Abstract

In asset management with uncertainty, a dynamic portfolio allocation problem to minimize the average rates of falling is discussed. Introducing coherent risk measures and average value-at-risks, this paper deals with portfolio optimization to make the asset management stable for a long term. These criteria are applied to fuzzy random variables by perception-based extension. In this model, randomness is estimated stochastically and fuzziness is evaluated by $$\lambda$$ -mean functions and evaluation weights. By mathematical programming and dynamic programming, dynamic optimality conditions with optimal portfolios are derived. A few numerical examples are given to compare the cases of coherent risk measures with other value-at-risks. It is observed that the presented portfolio optimization method with coherent risk measures gives stable asset management in a long term.