基于模糊值损益证券的期望效用优化分析

Analysis of expected utility maximization on securities with fuzzy valued payoffs

对由具有模糊值损益证券所构成市场中的期望效用优化问题进行了分析.在分析中使用了加权期望效用模型度量模糊值财富对应的期望效用,提出了模糊意义下的套利概念,证明了最优投资组合存在当且仅当市场不存在模糊意义下的套利机会,重点讨论了最优投资组合的性质,并利用最优组合描述了资产的当前价格.

The problem of maximizing the expected utility is analyzed in a market,where assets are modeled by their fuzzy valued payoffs.The weighted expected utility model is used for analysis and discussion.A concept of arbitrage in fuzzy sense is proposed.It is proved that the optimal portfolio exists if and only if the market has no arbitrage in fuzzy sense. Properties on the optimal portfolio are discussed,among which current prices of assets can be expressed by the optimal portfolio.