On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions
Freddy Delbaen (Department of Mathematics), Ying Hu (IRMAR), Adrien, Richou (IRMAR)
TL;DR
This paper extends the uniqueness results for quadratic backward stochastic differential equations (BSDEs) with convex generators to solutions with specific exponential moments, strengthening the nonlinear Feynman-Kac formula.
Contribution
It proves uniqueness of solutions with certain exponential moments, broadening the class of solutions where the nonlinear Feynman-Kac formula applies.
Findings
Uniqueness holds among solutions with given exponential moments.
Strengthens the nonlinear Feynman-Kac representation.
Extends previous results to less restrictive solution classes.
Abstract
In a previous work, P. Briand and Y. Hu proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved by P. Briand and Y. Hu.
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Taxonomy
TopicsStochastic processes and financial applications · Nonlinear Differential Equations Analysis · Stability and Controllability of Differential Equations