Based On Stable Preferences Under The Principle Of Including The Consumer's Utility Maximization Problem

In this article we consider the robust utility maximization problem of an agent with consumption and obtain some useful results. When an agent is evaluating his expected utility, he is uncertain about the correct subject probability measure. Instead the agent is faced with a whole set of conceivable probabilities. Robust preferences mean that the agent considers the infimum of all possible expectations in order to be on the safe side in an incomplete market. Stefan Weber and Anne Gundel considered the robust utility maximization problem without consumption and arrived at the optimal solutions in 2007. However, the robust utility maximization problem with consumption, as we know, has not been considered.First of all, Chapter 2 describes the utility maximization problem in a complete market and the robust utility maximization problem under a joint budget constraint and downside risk constraint in an incomplete market. Then, using duality theory, we get the solution of the robust utility maximization problem under a joint budget constraint and downside risk constraint.In Chapter 3, we consider the single-agent optimal consumption problem with robust preferences under budget constraint. The existence and uniqueness of the solution of the robust consumption problem are proved via the dual theory. Then we also get the existence and uniqueness of the solution to the model with risk constraints. Furthermore, in general market, we consider the robust optimal consumption problem with a number of agents, and then we derive that its solution exists and it's unique. This result can be regarded as the generalization of the result from Stefan Weber and Anne Gundel.