Optimal Consumption/Portfolio And Retirement Problem Under Different Agents' Assumption

This thesis investigates an agent's consumption/portfolio and retirement problem on different assumptions under the influence of labor on investor's utility. One case is the agent staying in leisure, and feeling like positive utility; while the other is disutiliy aroused by work. The former discusses decision-making problems, in which the dividend-pay-ment of risk assets is considered. For disutility, we research problem with dividend-payment, then the model with Knightian uncertainty and individual emotion is further discussed.Firstly, this thesis studies an agent's consumption-leisure, portfolio and retirement problem, which takes the dividend-payment of risk assets into account. The agent's utility is derived from consumption and leisure, which described by CES utility. The agent is able to adjust her supply of labor flexibly above a certain minimum work-hour, and also has a retirement option. The optimal retirement time can be characterized through optimal stopping time. Using the martingale method and the variational inequality, the optimal consumption-leisure, the portfolio strategy and the optimal retirement time of the agent are obtained. Secondly, considering the dividend process and an agent with disutility, we continue approaching the problem. The agent has a retirement option. By retirement, she avoids the utility loss but gives up labor income. Using the dynamic programming method to solve a free boundary value problem, we obtain an explicit solution for the critical wealth level, optimal consumption and portfolio strategy of the agent.Thirdly under the frame of disutility, Knightian uncertainty and ambiguity attitude are simultaneously considered. Knightian uncertainty and ambiguity attitude affect the decision-making behavior. Usingα-MEU model, we investigate how Knightian uncertainty and ambiguity attitude affect the consumption and portfolio strategy and the retirement choice of the agent. After giving an explicit solution for the agent's optimal consumption and portfolio strategy, we analyze the solution from a view of economics. According to investor's emotional situations, we classify investors into three cases:pessimist\optimist\temperate agent. We compare the amount of risk asset and the consumption rate for three cases. The results show that temperate agent's portfolio curve locates between pessimistic and optimistic. They can be explained as:the higher ambiguity attitude a, the lower the amount invested in risk asset, so critical wealth is less on retirement time. The consumption rate can be ordered as optimist> temperate agent> pessimist. Comparatively speaking, A pessimist allocates less wealth into risk asset, and shares lower consumption rate, which is in accord with the reality.