Study On Optimal Consumption And Portfolio With Uncertainty Of Stock Price Volatility

The models of optimal consumption and portfolio have recently been studied by many scholars, but most of them were based on risk assets (stock) assuming a constant rate of price volatility. As the financial markets continue to innovate and develop, more realistic model to study can not be ignored.Firstly, this thesis is based on the existing theories, considers the effect of the model uncertainty of stock price volatility on an investor’s optimal consumption and portfolio with a continuous-time model. By using HJB equation, the optimal policy is derived. An explicit solution of optimal consumption and investment decision is set up in the case of constant relative risk-aversion (CRRA) utility. Also get that the ambiguity averse investor is based on the upper bound of stock price volatility to make decision and the numerical simulation and its economic analysis are provided. Then the effect of the Knightian uncertainty of stock price volatility on an investor’s optimal consumption and portfolio under inflation is studied. An explicit solution of optimal consumption and investment decision under inflation is set up and the numerical simulation and its economic analysis are provided. Finally, the investor’s optimal consumption and portfolio with inflation obey mean reverting process is studied. By giving a stochastic differential equation of inflation with mean reverting process, the optimal consumption and investment decision is set up in the case of constant relative risk-aversion (CRRA) utility. This thesis characterizes he optimal consumption and portfolio which is affected by Knightian uncertainty, inflation and mean reverting.In a word, the theoretical value of this thesis is the explicit solution of optimal consumption and investment decision is set up when the stock price volatility is uncertain. Also get that the ambiguity averse investor is based on the upper bound of stock price volatility to make decision. The models of this thesis improve the traditional ones and have given a practical guidance for investors to choose the optimal consumption and portfolio, so these models take on certain actual application value.