Optimal Consumption And Portfolio With Dividends And Regime Switching Under Knightian Uncertainty

Based on the foundation of Merton and many other financial researchers’ studies, this article is the improvement and promotion of certain conclusions and examines a continuous-time intertemporal consumption and portfolio choice problem with ambiguity, where expected returns of a risky asset with dividend payments follow a hidden Markov chain. The content is divided into the following three parts:On the basis of the foreign and domestic research of optimal consumption and portfolio theory concerning with regime switching and Knightian uncertainty, we first portray the hidden Markov transition model under unobservable state formed by the expected return of the risky assets, that enables people to have a clear understanding of the way from its perceptual and actual financial markets on unobservable state to its precise mathematical model.Next we assume that investors with recursive multiple priors utility possess a set of priors for unobservable investment opportunities. The optimal consumption and portfolio policies are explicitly characterized in terms of the Malliavin derivatives and stochastic integral equations. Through a numerical simulation, we find that continuous Bayesian revisions under incomplete information generate ambiguity-driven hedging demands that mitigate intertemporal hedging demands. Moreover, ambiguity aversion magnifies the importance of hedging demands in the optimal portfolio policies. Again, the effect of the inflation and dividends on investment and consumption market has also been deliberated, that is to say, quantitative studies of the impact of different sizes of inflation and dividends on optimal portfolio are treated well.Finally, in order to better show the practicality of this article, Monte Carlo Malliavin derivative simulation calculations were put into utilization to illustrate the trends of optimal stock demand and intertemporal hedging demand under ambiguous situations and we consider the impact of inflation and dividends to investment as well. Through the expansion of the model, the conclusion was formulated better in accordance with economic realities.