On Study Of Optimal Consumption And Portfolio Under Knightian Uncertainty And Partial Information

In financial mathematics field, the optimal consumption and investment strategy problem is one of the basic problems, which has been studied by nu-merous international and domestic scholars. In the real economic environment, we not only consider the part information’s impact on the optimal consump-tion and investment strategy, but also consider the different attitudes held by the investors about the future prospects for investment which result in differ-ences of optimal consumption and investment strategy. Under Knightian un-certainty and partial information, this paper sets up optimal consumption and investment model by using stochastic optimal control method. Then we can derive an explicit representation of the optimal trading strategy which makes the maximization of the expected utility of investor’s consumption and termi-nal wealth. The establishment of these theories can guide practice very well.In the first of this paper, an optimal portfolio strategy is characterized un-der partial information with the dividend payment. We consider a multi-stock market model where prices satisfy a stochastic differential equation with in-stantaneous rates of return modeled as a continuous time Markov chain with finitely many states. For the investor’s objective of maximizing the expected utility of the terminal wealth, by using HMM filtering theory and Malliavin calculus we derive an explicit representation of the optimal trading strategy. Secondly, on the basis of the above content, we study the optimal trading s-trategy under the framework of the Knightian uncertainty. We characterize a model of α-maxmin expected utility(a-MEU). A main feature of our model is that it could differentiate between ambiguity and ambiguity attitude, ambiguity is described as the decision-maker’s subjective beliefs, and ambiguity attitude is described as the decision-maker’s tastes. For the Knightian uncertainty in-vestor’s objective of maximizing the a-maxmin expected utility of the terminal wealth, we derive an explicit representation of the optimal trading strategy. Fi- nally, an optimal consumption and portfolio is studied under Knightian uncer-tainty with the mean-reverting interest rate. This paper gives the representation of α-MEU by using the recursive multiple priors utility. The optimal portfolio is derived for power utility with the mean-reverting interest rate.Through the study of above problems, our model is more perfect and more in line with the actual than traditional Merton model. It has certain prac-tical guiding role for the investors who choose the optimal consumption and investment strategy in the market.