Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem
Computational Finance
2015-03-17 v1 Optimization and Control
Probability
Portfolio Management
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.
Keywords
Cite
@article{arxiv.1101.2968,
title = {Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem},
author = {Keita Owari},
journal= {arXiv preprint arXiv:1101.2968},
year = {2015}
}