Researches On Expected Utility With Fuzzy Payoff

This thesis describes the return of uncertain asset by fuzzy number and fuzzy random variable, introduces the weighted expected utility model about fuzzy and fuzzy random uncertain wealth for investor, and studies the problem of security portfolio selection and asset utility pricing.The problem of expected utility based the fuzzy returns is studied in this thesis. After defining the fuzzy expectation, the expected utility model with fuzzy value asset for investor is established. Investor is introduced with three characters:utility functionu, the initial endowment e and reservative attitude to uncertain phenomenon, after that, fuzzy expected utility model is established. Some properties of fuzzy expected utility are also studied, such as non decreasing, concavity and certainty equivalence. The question how to allocate money to fuzzy uncertain asset and certain asset is proposed and the way how to solve this problem is studied. The concept of "viable" market is defined, under the market, the optimal utility about multi fuzzy values assets is studied and the existence and properties of solution are analyzed. On the basis of properties of optimum solution, the relation between price and return of fuzzy asset is discussed. Finally a numeric example is given to introduce how the proposed model to be used in investment.The problem of fuzzy random expected utility in finite state space is studied. Because of defaults that uncertain be presented by fuzzy variable or random variable, fuzzy random variable is designed to character asset's return, the expected utility in fuzzy random environment is gave. Some properties and certainty equivalence of fuzzy random expected utility are studied and the common fuzzy random expected utility model is set up. The existence and proprieties of optimal solution in viable market are both analyzed, the relation between the price and return of fuzzy random asset is also studied.Fuzzy expected utility based on fuzzy theory is a new way to study utility theory,It can solve the problem of asset allocation successful by changing the uncertain to certain. The fuzzy random expected utility model based on fuzzy expected utility is better to adapt to reality investment, because it considers the random factor and fuzzy factor in investment, then it brings better invest strategy for investor by dealing with more market information and subject attitude of investor.