Mathematics – Probability
Scientific paper
2011-01-27
Mathematics
Probability
Scientific paper
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 $\mathbb{H}^1$ 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 (2000) on bounded solutions.
Barrieu Pauline
Karoui Nicole El
No associations
LandOfFree
Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-545393