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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
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 | ||||||
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| 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: |
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| Date of first compliant deposit: | 25 February 2019 | ||||||
| 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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