Portfolio Selection Based On A Recursive Utility Function And Optimal Consumption And Its Applications

Utility is a basic conception in microeconomics. Consumers buy some goods and consume it in order to obtain satisfactory. Speaking of utility function, people always use the utility additivity with respect to time and states of nature. But the utility is overly restrictive in time and states of nature. We will give an example to show it. So people begin to find out if there is another utility which is more practical and less complicated. That is the recursive utility function which we will discuss in this paper.In this paper, our purpose is to discuss the optimal consumption and portfolio selection with recursive utility under uncertainty and its application in security pricing. In the first part of this paper, we introduce briefly the background and recent research of recursive utility. Secondly, we represent the form of recursive utility which we will discuss in this paper and prove that it satisfies the general properties of utility. Under this base, we use the method of utility gradient and dynamics to present the asset pricing formula with maximizing the utility by portfolio selection and optimal consumption. Thirdly, we apply this formula into the optimal wealth distributions between two agents having recursive utility and the trust-agent problems under individual agent model. And we receive a property which cannot receive by additive utility. Fourthly, we extend the recursive utility to the continuous setting to achieve stochastic differential utility and use martingale method to discuss the maximum problem of both conception and last wealth under continuous security market. At last, we extend the finite horizon to the infinite horizon and present the form of stochastic differential utility under the infinite horizon.