Expected Utility-Risk Molds For Portfolio Selection Under Uncertainty

As a commonly used tool utility function is widely used in the financial industry, risk analysis, insurance pricing, portfolio decisions and management. This paper stud-ies the portfolio selection problem in uncertain environment under uncertainty theory, establishing three expected utility-risk models by three risk measurement tools, to make investors to make rational decision to realize benefit maximization.The basic framework is as follows:In the first part, we introduce the background and significance in the portfolio to maximize utility, the development of a representative at home and abroad regarding this aspect.In the second part, we introduce the preliminary knowledge of uncertainty theory and related knowledge of uncertain utility.In the third part, we measure risk by the variance to achieve expected utility max-imization and give expected utility-variance model, transformational model, example.In the fourth part, Variance reflects the deviation degree and not pointed out that deviate from the direction. The actual risk is brought by the negative deviation in the actual. In order to overcome the defects of variance, we use VaR (Value at Risk) to measure risk, for achieving expected utility maximization. First to gives the definition of VaR (Value at Risk) and related reasoning; second to establish expected utility-VaR model, transformational model; lastly example.In the fifth part, VaR is the biggest loss under a certain confidence level but not reflect the worst case loss and tail loss level. To better control risk, we have to measure risk by TVaR (Tail Value at Risk) to achieve expected utility maximization. At first the article puts forward the definition of TVaR (Tail Value at Risk) and related reasoning; lastly to establish expected utility-TVaR maximization model, transformational model, example.Finally, conclusion and some problems to be studied further are proposed in the thesis.