Research On Portfolios Based On Exponential Utility Function

At first, an exponential utility function has been devised by making use of the Mean-CVaR model and its efficient frontier. Subsequently, using the principle of maximizing utility, the Mean-CVaR model was converted to a model that can be directly solved by computer in an equity market where shorting sale is prohibited. By applying this exponential utility function, portfolios to suit a variety of different investors can be obtained.Secondly, in the case of not assuming the distribution of the yield, the expected utility approximate expression is derived by use of the actual sample rate of return, and the "Utility - CVaR" model under normal circumstances is established with function F which was established by Rockafeller, and than the solving method of the model is pointed out.Finally, this paper introduces the Spectral measure of risk and the relationship among the Spectral measure of risk, VaR and CVaR. By introducing the exponential utility function, the expression of the Spectral measure of risk under exponential utility function is derived, and the "Exponential spectral risk measure" portfolio model is established, and than the difficulty of solving this model is pointed out.