Invariance times
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Stéphane Crépey [1]
;
Shiqi Song
[1]
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[1] University of Paris-Saclay
University of Paris-Saclay
Arrondissement de Palaiseau, Francia
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 2, 2017, págs. 4632-4674
- Idioma: inglés
- DOI: 10.1214/17-AOP1174
- Enlaces
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Resumen
On a probability space (Ω,A,Q)(Ω,A,Q), we consider two filtrations F⊂GF⊂G and a GG stopping time θθ such that the GG predictable processes coincide with FF predictable processes on (0,θ](0,θ]. In this setup, it is well known that, for any FF semimartingale XX, the process Xθ−Xθ− (XX stopped “right before θθ”) is a GG semimartingale. Given a positive constant TT, we call θθ an invariance time if there exists a probability measure PP equivalent to QQ on FTFT such that, for any (F,P)(F,P) local martingale XX, Xθ−Xθ− is a (G,Q)(G,Q) local martingale. We characterize invariance times in terms of the (F,Q)(F,Q) Azéma supermartingale of θθ and we derive a mild and tractable invariance time sufficiency condition. We discuss invariance times in mathematical finance and BSDE applications.
