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Mathematics > Probability

arXiv:1812.03526 (math)
[Submitted on 9 Dec 2018 (v1), last revised 13 Sep 2020 (this version, v4)]

Title:Path Dependent Optimal Transport and Model Calibration on Exotic Derivatives

Authors:Ivan Guo, Gregoire Loeper
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Abstract:In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path dependent partial differential equations (PPDEs). Moreover, we provide a dimension reduction result based on the new notion of "semifiltrations", which identifies appropriate Markovian state variables based on the constraints and the cost function. Our technique is then applied to the exact calibration of volatility models to the prices of general path dependent derivatives.
Subjects: Probability (math.PR); Optimization and Control (math.OC); Mathematical Finance (q-fin.MF)
Cite as: arXiv:1812.03526 [math.PR]
  (or arXiv:1812.03526v4 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.03526

Submission history

From: Ivan Guo [view email]
[v1] Sun, 9 Dec 2018 17:19:46 UTC (1,754 KB)
[v2] Sat, 15 Jun 2019 10:50:07 UTC (1,759 KB)
[v3] Thu, 6 Aug 2020 15:49:38 UTC (1,765 KB)
[v4] Sun, 13 Sep 2020 05:15:28 UTC (1,764 KB)
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