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The left-curtain martingale coupling in the presence of atoms

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Hobson, David G. and Norgilas, Dominykas (2019) The left-curtain martingale coupling in the presence of atoms. The Annals of Applied Probability, 29 (3). pp. 1904-1928. doi:10.1214/18-AAP1450

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Official URL: http://dx.doi.org/10.1214/18-AAP1450

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Abstract

Beiglböck and Juillet (Ann. Probab. 44 (2016) 42–106) introduced the left-curtain martingale coupling of probability measures μ and ν, and proved that, when the initial law μ is continuous, it is supported by the graphs of two functions. We extend the later result by constructing the generalised left-curtain martingale coupling and show that for an arbitrary starting law μ it is characterised by two appropriately defined lower and upper functions.

As an application of this result, we derive the model-independent upper bound of an American put option. This extends recent results of Hobson and Norgilas (2017) on the atom-free case.

Item Type: Journal Article
Divisions: Faculty of Science > Statistics
Journal or Publication Title: The Annals of Applied Probability
Publisher: Institute of Mathematical Statistics
ISSN: 1050-5164
Official Date: 19 February 2019
Dates:
DateEvent
19 February 2019Available
1 December 2018Accepted
Volume: 29
Number: 3
Page Range: pp. 1904-1928
DOI: 10.1214/18-AAP1450
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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