Study On Optimal Consumption And Portfolio With Inflation

The models of optimal consumption and portfolio have recently been studied by many scholars, but most of them were based on the basic assumptions of Merton model, and a number of improvements were made. As the financial markets continue to innovate and develop, the current models need to be extended.Firstly, this thesis is based on the existing theories, considers optimal consumption and portfolio investment problems of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to inflation and dividend when the investor fully observes the basket price. By using HJB equation, the optimal policy is derived, and the modified Mutual Fund Theorem consisting of three funds is obtained in theory. Secondly, in the particular case of constant relative risk-aversion (CRRA) utility, an explicit solution of the optimal consumption and portfolio policy is provided. When consumption basket prices are partially observed, we considers optimal consumption and portfolio investment problems of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to inflation and dividend. By using the method of random optimal control and filtering theory to establish the optimal consumption and portfolio model, the modified Mutual Fund Theorem consisting of three funds is obtained. In the particular case of constant relative risk-aversion (CRRA) utility, an explicit solution of the optimal consumption and portfolio policy is provided. And numerical example shows that the payment of dividends will influence optimal consumption and portfolio of an investor. Thirdly, this thesis studies the optimal consumption and portfolio choice of investor who differentiates ambiguity and ambiguity attitude under Knightian uncertainty or ambiguity with inflation in the case of fully observed consumption basket prices. By adoptingα-maxmin expected utility (α-MEU) and the technique of backward stochastic differential equation (BSDE) and using HJB equation, the optimal policies are derived, and the modified Mutual Fund Theorem consisting of three funds is obtained. In the special case of constant relative risk-aversion (CRRA) utility, this thesis characterizes the optimal portfolio which is affected by ambiguity and inflation.In a word, the theoretical value of this thesis rests with establishing the modified Mutual Fund Theorem, which clearly shows the allocations of the optimal portfolio in these funds and the proportions of the wealth invested in these funds. 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.