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

TL;DR

This paper extends convex duality methods to robust utility maximization with unbounded claims, establishing a duality relation for a broad class of utility functions using a robust version of Rockafellar's theorem.

Contribution

It introduces a robust extension of Rockafellar's theorem to handle unbounded claims in utility maximization, broadening the applicability of duality methods.

Findings

Duality relation holds for unbounded claims and utility functions on the entire real line.

Proves a robust version of Rockafellar's theorem for convex integral functionals.

Applies Fenchel's duality theorem to establish the main results.

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.