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Quantitative Finance > Mathematical Finance

arXiv:2204.12250 (q-fin)
[Submitted on 26 Apr 2022]

Title:Martingale Schrödinger Bridges and Optimal Semistatic Portfolios

Authors: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 Schrödinger 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.
Subjects: Mathematical Finance (q-fin.MF); Probability (math.PR)
MSC classes: 91G10, 60G42, 60H05, 94A17, 26B40
Cite as: arXiv:2204.12250 [q-fin.MF]
  (or arXiv:2204.12250v1 [q-fin.MF] for this version)
  https://doi.org/10.48550/arXiv.2204.12250

Submission history

From: Johannes Wiesel [view email]
[v1] Tue, 26 Apr 2022 12:03:26 UTC (23 KB)
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