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May 2018 From optimal stopping boundaries to Rost’s reversed barriers and the Skorokhod embedding
Tiziano De Angelis
Ann. Inst. H. Poincaré Probab. Statist. 54(2): 1098-1133 (May 2018). DOI: 10.1214/17-AIHP833

Abstract

We provide a new probabilistic proof of the connection between Rost’s solution of the Skorokhod embedding problem and a suitable family of optimal stopping problems for Brownian motion, with finite time-horizon. In particular we use stochastic calculus to show that the time reversal of the optimal stopping sets for such problems forms the so-called Rost’s reversed barrier.

Nous donnons une nouvelle preuve probabiliste de la relation entre la solution de Rost du problème de plongement de Skorokhod et une famille convenable de problèmes d’arrêt optimal pour le mouvement Brownien, à horizon de temps fini. En particulier, nous utilisons le calcul stochastique pour montrer que le retourné en temps des ensembles d’arrêt optimal forme ce qu’on appelle la barrière de Rost retournée.

Citation

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Tiziano De Angelis. "From optimal stopping boundaries to Rost’s reversed barriers and the Skorokhod embedding." Ann. Inst. H. Poincaré Probab. Statist. 54 (2) 1098 - 1133, May 2018. https://doi.org/10.1214/17-AIHP833

Information

Received: 2 June 2016; Revised: 13 March 2017; Accepted: 26 March 2017; Published: May 2018
First available in Project Euclid: 25 April 2018

zbMATH: 06897980
MathSciNet: MR3795078
Digital Object Identifier: 10.1214/17-AIHP833

Subjects:
Primary: 35R35, 60G40, 60J55, 60J65

Rights: Copyright © 2018 Institut Henri Poincaré

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Vol.54 • No. 2 • May 2018
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