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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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.

Résumé

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1524643241

Digital Object Identifier
doi:10.1214/17-AIHP833

Mathematical Reviews number (MathSciNet)
MR3795078

Zentralblatt MATH identifier
06897980

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.aihp/1524643241


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