Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem

2011/01/15 by Keita Owari, Owari, Keita
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #49N15 #60G80 #60H05 #91G10 #91G80 #Computational Finance (q-fin.CP) #Decision-Making and Behavioral Economics #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Risk and Portfolio Optimization #math.OC #math.PR #msc:49N15 #msc:60G80 #msc:60H05 #msc:91G10 #msc:91G80 #q-fin.CP #q-fin.PM

paper · pdf · doi:10.48550/arxiv.1101.2968

arxiv created 2011/01/15 · openalex publication_date 2011/01/15 · arxiv updated 2015/03/17 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endowment. To obtain this duality, we prove a robust version of Rockafellar's theorem on convex integral functionals and apply Fenchel's general duality theorem.

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