[hal-00391112, v1] On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions
نویسندگان
چکیده
In [4], the authors 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 in [4].
منابع مشابه
On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case
In F. Delbaen, Y. Hu and A. Richou (Ann. Inst. Henri Poincaré Probab. Stat. 47(2):559–574, 2011), the authors proved that uniqueness of solution to quadratic BSDE with convex generator and unbounded terminal condition holds among solutions whose exponentials are Lp with p bigger than a constant γ (p > γ). In this paper, we consider the critical case: p = γ. We prove that the uniqueness holds am...
متن کاملQuadratic BSDEs with convex generators and unbounded terminal conditions
In [3], the authors 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. Unde...
متن کاملOn the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions
In [4], the authors 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 in [4].
متن کاملA note on the existence of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition
In [17], the author proved the existence and the uniqueness of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition when the generator and the terminal condition are locally Lipschitz. In this paper, we prove that the existence result remains true for these BSDEs when the regularity assumptions on the terminal condition is weakened.
متن کامل[hal-00327496, v1] Uniqueness results for convex Hamilton-Jacobi equations under $p>1$ growth conditions on data
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+ |x|p) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superli...
متن کامل