Optimal Consumption And Portfolio Policies Under Early Retirement

The domestic and foreign scholars have already made the research on early retirement. Based on previous papers, this paper studies optimal consumption and portfolio choices, considering three different cases, in a framework where investors adjust their labor supply through an irreversible choice of retirement time. The optimal portfolio and the optimal retirement time show that the agent can not only accumulate wealth for the early retirement, but also enjoy the consumption and leisure.First, we consider the case with the dividend payment of the stock. In this financial market, we study the optimal portfolio and early retirement problems of the economic agents. We introduce the utility function on consumption and leisure of the economic agents. Through using the method of stochastic control, the expected utility maximization of consumption-leisure utility is discussed and optimal strategies are obtained. In order to highlight our more realistic results, numerical analysis and economics explanations are given, and the related graphics are also given.Next, we consider the agent differentiating ambiguity and ambiguity attitude. Single probability measure can not explain the Knight uncertainty, so we consider the stochastic differential utility of the agent in a more general set of probability measure. Introducing the a-MEU can help differentiating ambiguity and ambiguity attitude. By using the backward stochastic differential equations (BSDE) theory and the martingale method, we can obtain the optimal consumption and portfolio strategies. Meanwhile, the numerical results show that both ambiguity and ambiguity attitude affect the optimal consumption and portfolio policies.Finally, we consider the agent of borrowing constraint conditions under Knightian uncertainty. We extend the case of the agent borrowing against the value of his future labor income to the one of the agent not being permitted to borrow against the value of future income. Thus, based our model, the obtained results explain well the phenomena in the real world.