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Quasi-sure Stochastic Analysis through Aggregation

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Quasi-sure Stochastic Analysis through Aggregation
2.	Creator	Author's name, affiliation, country	Mete H Soner; Swiss Finance Institute
2.	Creator	Author's name, affiliation, country	Nizar Touzi; Ecole Polytechnique Paris
2.	Creator	Author's name, affiliation, country	Jianfeng Zhang; University of Southern California
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	non-dominated probability measures, weak solutions of SDEs, uncertain volatility model, quasi-sure stochastic analysis
3.	Subject	Subject classification	60H10, 60H30
4.	Description	Abstract	This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic representations of fully nonlinear partial differential equations and applications to mathematical finance. The existing literature relies either on the capacity theory (Denis and Martini), or on the underlying nonlinear partial differential equation (Peng). In both approaches, the resulting theory requires certain smoothness, the so-called quasi-sure continuity, of the corresponding processes and random variables in terms of the underlying canonical process. In this paper, we investigate this question for a larger class of ``non-smooth" processes, but with a restricted family of non-dominated probability measures. For smooth processes, our approach leads to similar results as in previous literature, provided the restricted family satisfies an additional density property.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-10-14
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/950
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-950
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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