Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios
Abstract
In a two-period financial market where a stock is traded dynamically and European options at maturity are traded statically, we study the so-called martingale Schr\"odinger bridge Q*; that is, the minimal-entropy martingale measure among all models calibrated to option prices. This minimization is shown to be in duality with an exponential utility maximization over semistatic portfolios. Under a technical condition on the physical measure P, we show that an optimal portfolio exists and provides an explicit solution for Q*. This result overcomes the remarkable issue of non-closedness of semistatic strategies discovered by Acciaio, Larsson and Schachermayer. Specifically, we exhibit a dense subset of calibrated martingale measures with particular properties to show that the portfolio in question has a well-defined and integrable option position.
Keywords
Cite
@article{arxiv.2204.12250,
title = {Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios},
author = {Marcel Nutz and Johannes Wiesel and Long Zhao},
journal= {arXiv preprint arXiv:2204.12250},
year = {2022}
}