Discretionary stopping in an optimal consumption and portfolio seletion problem

Abstract

This thesis studies various discretionary stopping problems in a consumption and portfolio selection problem. The difference between the discretionary stopping problem and the classical consumption/investment problem is that the economic model allows the agent can stop freely before a prescribed time. Karatzas and Wang (2000) first studied a discretionary stopping problem in the context of optimal consumption and portfolio selection. Chapter 3 provides the theoretical motivation and its extension to the case where the economic agent has stochastic differential utility by using backward stochastic differential equations. As an application, Chapter 4 deals with the decision problem of a risk and ambiguous-averse agent with utility loss from active management to switch from active asset management to passive asset management. Chapter 5 studies the effect of the preference change in a discretionary stopping problem. Chapter 6 studies a problem of a wage earner to retire from work and to become a full-time investor.