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 exten- sion. In this model, randomness is estimated stochastically and fuzziness is evaluated by -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. Keywords Portfolio optimization · Coherent risk measure · Average value-at-risk · Fuzzy random variable · Perception- based extension · Dynamic programming 1 Introduction shortfall, and entropic value-at-risk (Rockafellar and Uryasev 2000; Tasche 2002). Kusuoka (2001) gave a spec- In financial engineering, the portfolio is one of the most use- tral representation for coherent risk measures, and Acerbi ful allocation techniques for asset management. In dynamic (2002); Adam (2008) discussed its applications to portfo- optimization with portfolio allocation, the minimization of lio
Granular Computing – Springer Journals
Published: Jun 5, 2018
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