Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

From optimal stopping boundaries to Rost’s reversed barriers and the Skorokhod embedding

Tiziano De Angelis

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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.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 2 (2018), 1098-1133.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J65: Brownian motion [See also 58J65] 60J55: Local time and additive functionals 35R35: Free boundary problems

Optimal stopping Skorokhod embedding Rost’s barriers Free-boundary problems


De Angelis, Tiziano. From optimal stopping boundaries to Rost’s reversed barriers and the Skorokhod embedding. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 2, 1098--1133. doi:10.1214/17-AIHP833.

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