Convex duality and Orlicz spaces in expected utility maximization
Optimization and Control
2020-01-07 v5
Abstract
In this paper we report further progress towards a complete theory of state-independent expected utility maximization with semimartingale price processes for arbitrary utility function. Without any technical assumptions we establish a surprising Fenchel duality result on conjugate Orlicz spaces, offering a new economic insight into the nature of primal optima and providing fresh perspective on the classical papers of Kramkov and Schachermayer (1999, 2003). The analysis points to an intriguing interplay between no-arbitrage conditions and standard convex optimization and motivates study of the Fundamental Theorem of Asset Pricing (FTAP) for Orlicz tame strategies.
Cite
@article{arxiv.1711.09121,
title = {Convex duality and Orlicz spaces in expected utility maximization},
author = {Sara Biagini and Aleš Černý},
journal= {arXiv preprint arXiv:1711.09121},
year = {2020}
}
Comments
v5: added thanks; fixed typo in the definition of L^{\hat U}