Optimal Consumption And Portfolio Choice Under Model Uncertainty

With the development of a financial market, optimal consumption and portfolio problem is noted by many scholars. And a number of domestic and foreign scholars have some research on optimal consumption and investment model from the different views, however most of them establish the model of a financial market for an optimal investment strategy, which is fully trusted by an investor. However, with the innovation and development of the financial market, the model has an uncertainty, moreover a realistic investment model is worth researching. Therefore, based on the existing theoretical results, combined with the development of the current economic environment, the impact of model uncertainty on optimal consumption and portfolio is analyzed. Under the framework of the misspecification of the model, considering the factors of inflation and dividend payments, through the use of stochastic optimal control method to establish the optimal consumption and portfolio model, we provide a real economic analysis.Firstly, we investigate the case of stock dividend payments under model uncertainty. The optimal consumption and portfolio for an investor with recursive preferences are described. An investor worried about model misspecification, so the robust decision rules are sought.In the case of a financial market with expected returns of stocks following a mean-reverting process, we derive an exact analytical solution of the optimal consumption and portfolio on condition that an investor’s intertemporal elasticity of substitution is equal to one and the risk aversion is moderate. Given negative correlation between stock returns and expected returns, through a numerical analysis, it was found that the aversion to model uncertainty increases the proportion of wealth invested in stocks, and the payments of stock dividends further increase the proportion of wealth invested in stocks.Next, we discuss the model with the inflationary environment under model uncertainty. The impact of inflation volatility on optimal consumption and portfolio model under different inflationary environments is studied. The corresponding HJB equation of an investor’s value function is derived. For a special utility function, the exact analytical solution for optimal consumption and investment decisions is obtained. Through a numerical simulation, we find that the concern about model uncertainty lead to a substantial reduction of the myopic demand, causing the decline of the optimal equity allocation. However, taking into account the impact of low inflation volatility relative to the non-inflationary, inflation hedge demand increases the optimal equity allocation; when considering the impact of high inflation volatility relative to the non-inflationary, inflation hedge demand exacerbates the decline of the optimal equity allocation.