On the Stability of Utility Maximization Problems

Details On the Stability of Utility Maximization Problems On the Stability of Utility Maximization Problems

2010-10-20

arxiv.org/abs/1010.4322v4

Economy

Quantitative Finance

Portfolio Management

Keywords: Utility maximization, incomplete markets, stability, convex analysis for functions from $L^0$ to $L^0$, convex compa

Scientific paper

In this paper we extend the stability results of [4]}. 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 [7] plays an important role in our analysis.

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