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Monotone stability of quadratic semimartingales with applications to general quadratic BSDEs

Barrieu, Pauline 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

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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
Library of Congress subject classification: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Sets: Departments > Statistics
Research centres and groups > Centre for the Analysis of Time Series (CATS)
Research centres and groups > Risk and Stochastics Group
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 09 Mar 2012 15:29
URL: http://eprints.lse.ac.uk/42419/

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