A note on the existence of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition

Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition

Backward SDEs with superquadratic growth

In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the associated BSDE does not admit any bounded solution. On the other hand, we prove that if the superquadratic BSDE admits a bounded solution, then there exist infin...

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...

Two algorithms for the discrete time approximation of Markovian backward stochastic differential equations under local conditions

Two discretizations of a novel class of Markovian backward stochastic differential equations (BSDEs) are studied. The first is the classical Euler scheme which approximates a projection of the processes Z, and the second a novel scheme based on Malliavin weights which approximates the mariginals of the process Z directly. Extending the representation theorem of Ma and Zhang [MZ02] leads to adva...

BSDEs with Singular Terminal Condition and a Control Problem with Constraints

We provide a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a Backward Stochastic Differential Equation (BSDE). The novelty of our solution approach is that the BSDE possesses a singular terminal condition. We prove that a solution of the BSDE exists, thus partly generalizing existence results obtained by Popier in [9] and [10]. We perf...