Translator Disclaimer
June 2019 The left-curtain martingale coupling in the presence of atoms
David G. Hobson, Dominykas Norgilas
Ann. Appl. Probab. 29(3): 1904-1928 (June 2019). DOI: 10.1214/18-AAP1450

Abstract

Beiglböck and Juillet (Ann. Probab. 44 (2016) 42–106) introduced the left-curtain martingale coupling of probability measures $\mu$ and $\nu$, and proved that, when the initial law $\mu$ 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 $\mu$ 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.

Citation

Download Citation

David G. Hobson. Dominykas Norgilas. "The left-curtain martingale coupling in the presence of atoms." Ann. Appl. Probab. 29 (3) 1904 - 1928, June 2019. https://doi.org/10.1214/18-AAP1450

Information

Received: 1 March 2018; Revised: 1 October 2018; Published: June 2019
First available in Project Euclid: 19 February 2019

zbMATH: 07057470
MathSciNet: MR3914560
Digital Object Identifier: 10.1214/18-AAP1450

Subjects:
Primary: 60G42
Secondary: 60G40

Rights: Copyright © 2019 Institute of Mathematical Statistics

JOURNAL ARTICLE
25 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.29 • No. 3 • June 2019
Back to Top