BSDEs with weak terminal condition

BSDEs with weak terminal condition

We introduce a new class of Backward Stochastic Differential Equations in which the T -terminal value YT of the solution (Y, Z) is not fixed as a random variable, but only satisfies a weak constraint of the form E[Ψ(YT )] ≥ m, for some (possibly random) non-decreasing map Ψ and some threshold m. We name them BSDEs with weak terminal condition and obtain a representation of the minimal time t-va...

Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition

Bsdes with Stochastic Lipschitz Condition

We prove an existence and uniqueness theorem for backward stochastic di erential equations driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one.

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...

A 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.