Study On Optiamal Consumption And Portfolio Problem With Labor Income

In the financial field, optimal consumption and portfolio problem has attracted much attention, is one of the most basic research issues at the domestic and foreign. In recent years, researchers have focused more on consumption and portfolio strategies of investors choice, such as labor income. However, in real life, investors have to face a variety of backgrounds, these risks also affect investors’choice of consumption and portfolio strategies, such as inflation factors. So, we introduce inflation into the model of of optimal consumption and portfolio with labor income. On the other hand, investors often face two kinds of uncertainty:the first one can be called a risk prediction uncertainty, and the second is called the Knight uncertainty or ambiguity (ambiguity) is the real uncertainty. Since the uncertainty of the impact is often much higher than the impact of risk, so we consider the impact of Knight uncertainty on the optimal consumption and portfolio with labor income.This thesis is focus on the impact of both the inflation and Knight uncertainty on the consumption and portfolio of the investor on the basis of labor income. First of all, we take inflation into account in our model.Then by using the stochastic dynamic programming method, we obtain the HJB equation, and the optimal consumption and portfolio strategy is obtained. Finally, we quantitatively analyze the impact of the inflation and different labor income level on consumption and portfolio strategy.Secondly, the optimal consumption and portfolio problem with labor income is studied in the case of Knight uncertainty, Knight uncertainty is characterized by G-Brown motion, we deduce the corresponding HJB (Hamilton-Jacobi-Bellman) equation of the value function through the stochastic calculus and the stochastic dynamic programming method under nonlinear expectations.Finally, the numerical analysis shows that moderate inflation will boost consumption, but with the increase in the expected rate of inflation, for a risk appetite for investment, it will make use of high-risk and high return principle, and further increase investment in risky assets, from less consumption; investors are worried about Knight uncertainty led to less investment in risky assets, in order to avoid the high risk of investment.