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      On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case

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          Abstract

          In [3], the authors proved that uniqueness holds among solutions whose exponentials are \(L^p\) with \(p\) bigger than a constant \(\gamma\) (\(p\textgreater{}\gamma\)). In this paper, we consider the critical case: \(p=\gamma\). We prove that the uniqueness holds among solutions whose exponentials are \(L^\gamma\) under the additional assumption that the generator is strongly convex.

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          Lp solutions of backward stochastic differential equations

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            BSDE with quadratic growth and unbounded terminal value

            In this paper, we study the existence of solution to BSDE with quadratic growth and unbounded terminal value. We apply a localization procedure together with a priori bounds. As a byproduct, we apply the same method to extend a result on BSDEs with integrable terminal condition.
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              Quadratic BSDEs with convex generators and unbounded terminal conditions

              In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context.
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                Author and article information

                Journal
                2013-03-20
                2015-01-19
                Article
                1303.4859
                c59ac84a-85ad-4ac0-8204-9a67f23a2b6b

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.PR
                ccsd

                Probability
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