Research Of Portfolio Models Under Maximum Of Expected Utility

The construction of portfolio model is not only playing a crucial role in the process of investors’ optimal decision, but also one of the most important problems in financial economics, especially in asset pricing. When facing stochastic uncertainty factors in real capital market, expected utility theory is the most efficient research method. It has the idea that final expected utility, not the final wealth is what investors pursue. Based on the above concept, several portfolio models are built. Main contents and consequences are listed as follows.(1) The relationships between higher moment risk and expected wealth utility are revealed by using Taylor series expansion when utility function is the type of CARA. Skewness is positively related to expected wealth utility, and kurtosis is negatively related to expected wealth utility. At the same time, it is found that mean-variance portfolio model is equivalent to expected utility model under the conditions of quadratic utility function and normal distribution. In addition, a static model about CARA utility function is built and its simplified implicit solution is derived. (2) Fuzzy theory is more proper than expected utility theory when it is faced with nonrandom uncertainty factors. A fuzzy portfolio model is constructed considering portfolio’s liquidity, and then optimal solution and numerical results are given.(3) Dynamic models in three different assumed environment targeting maximum of cumulative expected utility during the whole investment period are formulated at last. And it will be found that optimal investment proportion is independent of the level of wealth, consumption or noncapital income. Moreover, optimal consumption level is determined by investor’s wealth level.