A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options

Alfred Galichon (), Pierre Henri-Labordère and Nizar Touzi
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Alfred Galichon: ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique
Nizar Touzi: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows us to recover previously known results about lookback options. In particular, our methodology induces a new proof of the optimality of Azéma–Yor solution of the SEP for a certain class of lookback options. Unlike the SEP technique, our approach applies to a large class of exotics and is suitable for numerical approximation techniques.

Keywords: convex duality; optimal control; volatility uncertainty (search for similar items in EconPapers)
Date: 2014-02
Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03460952v1
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Citations: View citations in EconPapers (19)

Published in The Annals of Applied Probability, 2014, 24 (1), pp.312-336. ⟨10.1214/13-AAP925⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03460952

DOI: 10.1214/13-AAP925

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