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Optimal stopping time problem in a general framework

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1.	Title	Title of document	Optimal stopping time problem in a general framework
2.	Creator	Author's name, affiliation, country	Magdalena Kobylanski; Université de Paris-Est Marne-la-Vallée; France
2.	Creator	Author's name, affiliation, country	Marie-Claire Quenez; Université Denis Diderot; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	optimal stopping ; supermartingale ; american options
3.	Subject	Subject classification	60G40
4.	Description	Abstract	We study the optimal stopping time problem $v(S)={\rm ess}\sup_{\theta \geq S} E[\phi(\theta)|\mathcal{F}_S]$, for any stopping time $S$,  where the reward is given by a family $(\phi(\theta),\theta\in\mathcal{T}_0)$ \emph{of non negative random variables} indexed by stopping times. We solve the problem under weak assumptions in terms of integrability and regularity of the reward family. More precisely, we only suppose $v(0) < + \infty$ and $(\phi(\theta),\theta\in \mathcal{T}_0)$ upper semicontinuous along stopping times in expectation. We show the existence of an optimal stopping time and obtain a characterization of the minimal and the maximal optimal stopping times. We also provide some local properties of the value function family. All the results are written in terms of families of random variables and are proven by only using classical results of the Probability Theory
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	INRIA
7.	Date	(YYYY-MM-DD)	2012-08-29
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2262
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-2262
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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