Martingale Schrödinger bridges and optimal semistatic portfolios

Marcel Nutz (), Johannes Wiesel () and Long Zhao ()
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Marcel Nutz: Columbia University
Johannes Wiesel: Columbia University
Long Zhao: Columbia University

Finance and Stochastics, 2023, vol. 27, issue 1, No 7, 233-254

Abstract: 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 ∗ $Q_{*}$ , that is, the minimal-entropy martingale measure among all models calibrated to option prices. This minimisation is shown to be in duality with an exponential utility maximisation over semistatic portfolios. Under a technical condition on the physical measure P $P$ , we show that an optimal portfolio exists and provides an explicit solution for Q ∗ $Q_{*}$ . This result overcomes the remarkable issue of non-closedness of semistatic strategies discovered by Acciaio et al. (Finance Stoch. 21:741–751, 2017). 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: Martingale Schrödinger bridge; Semistatic trading; 91G10; 60G42; 60H05; 94A17; 26B40 (search for similar items in EconPapers)
JEL-codes: C61 C65 G11 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00780-022-00490-x

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