Dynamic optimization of value-at-risk portfolios with fuzziness in asset management

Abstract

Using fuzzy random variables, a dynamic portfolio model with uncertainty is mentioned for object system. In this approach, the random property is numerated by stochastic expectation and the fuzzy property is also numerated by weights and mean functions. A value-at-risk is introduced to assess the risk of unfavorable paths in investment. Using dynamic programming and mathematical programming, the optimal solutions of a dynamic portfolio problem with VaR is mentioned. An optimization equation is derived and the optimal portfolios are given at each period.