On the Stability of Utility Maximization Problems
In this paper we extend the stability results of }. Our utility maximization problem is defined as an essential supremum of conditional expectations of the terminal values of wealth processes, conditioned on the filtration at the stopping time $\tau$. To establish our results, we extend the classical results of convex analysis to maps from $L^0$ to $L^0$. The notion of convex compactness introduced in  plays an important role in our analysis.
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