On the Stability of Utility Maximization Problems

2010/10/20 by Erhan Bayraktar, Bayraktar, Erhan, Ross Kravitz +1
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Mathematical Dynamics and Fractals #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #q-fin.PM

paper · pdf · doi:10.48550/arxiv.1010.4322

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

openalex publication_date 2010/10/20 · arxiv created 2011/03/25 · arxiv updated 2011/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 τ. To establish our results, we extend the classical results of convex analysis to maps from L⁰ to L⁰. The notion of convex compactness introduced in [7] plays an important role in our analysis.

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