Optimal Portfolio And Consumption Rules Under Partial Information

There is uncertainty in the actual environment of the economy, such as innovations in technique, introduction of new products, natural disasters, changes in law and government policies, the financial crisis and so on. The relationships among these events and the appreciation rate of risky assets are very complicated, and the uncertainty may bring great influence on the appreciation rate of risky assets. For the Markowitz classic portfolio selection and asset pricing theory, it is assumed the investor knows the expected return rate and the volatility of the risky assets. This assumption, however, is not fulfilled in practice. In order to use more accurate asset pricing model to describe the actual circumstances, we study optimal consumption and portfolio selection problem in which the mean return rate of a risky asset is unobservable.In this paper we first study optimal consumption and portfolio selection with incomplete information which is based on the Gennotte model. We compute the optimal consumption and portfolio policies of an investor with exponential utility and make a numerical analysis for different parameters change. The analysis results show that the risk-aversion coefficient, time horizon, the mean square error of the estimate, the price volatility impact optimal consumption and portfolio selection in different trends.Then we study optimal consumption and portfolio selection for a setting in which the mean return rate of a risky asset depend on an unobservable regime variable of the economy, which is defined as a continuous-time Markov chain. The investor estimates the current regime by observing past and present asset prices. We compute the optimal consumption and portfolio policies of an investor with exponential utility. The optimal consumption and portfolio rule of a long-time-horizon investor could be substantially different from that of a short-time-horizon investor. The difference is caused by an investor’s hedging demand of assets against fluctuations in the estimated mean returns.Finally, we analyze the consequences of heterogeneous beliefs to consumption. We suppose that an economy where all but one agent have the same beliefs is considered. This part shows that, depending on their specific nature, heterogeneous beliefs can lead to different patterns of equilibrium consumption. Two types of heterogeneous beliefs are distinguished:relative optimism/pessimism and confidence. It is demonstrated that when the agent is more optimistic than the market, he consumes more in good states of nature. When the agent is more confident about his estimate than the market, he consumes more in inner states of nature.