Barrieu, Pauline 
ORCID: 0000-0001-9473-263X and El Karoui, Nicole
(2013)
Monotone stability of quadratic semimartingales with applications to general quadratic BSDEs.
Annals of Probability, 41 (3B).
pp. 1831-1863.
ISSN 0091-1798
Abstract
In this paper, we study the stability and convergence of some general quadratic semimartingales. Motivated by financial applications, we study simultaneously the semimartingale and its opposite. Their characterization and integrability properties are obtained through some useful exponential submartingale inequalities. Then, a general stability result, including the strong convergence of the martingale parts in various spaces ranging from H1 to BMO, is derived under some mild integrability condition on the exponential of the terminal value of the semimartingale. This can be applied in particular to BSDE-like semimartingales. This strong convergence result is then used to prove the existence of solutions of general quadratic BSDEs under minimal exponential integrability assumptions, relying on a regularization in both linear-quadratic growth of the quadratic coefficient itself. On the contrary to most of the existing literature, it does not involve the seminal result of Kobylanski [Ann. Probab. 28 (2010) 558–602] on bounded solutions.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.imstat.org/aop/ |
| Additional Information: | © 2013 Institute of Mathematical Statistics |
| Divisions: | Statistics Centre for Analysis of Time Series |
| Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
| Date Deposited: | 09 Mar 2012 15:29 |
| Last Modified: | 23 Oct 2024 17:27 |
| URI: | http://eprints.lse.ac.uk/id/eprint/42419 |
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