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arXiv · 2204.12250

Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios

Marcel Nutz·Johannes Wiesel·Long Zhao
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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.

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Marcel Nutz, Johannes Wiesel, Long Zhao. 2022-04-26. Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios. https://arxiv.org/abs/2204.12250

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