Abstract
We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminf _{tto T} Y(t) = xi = Y(T). Hence, we extend known results for a non-Markovian terminal condition.
Highlights
In this paper, we consider a filtered probability space (, F, F, P) with a complete and right-continuous filtration F = {Ft, t ≥ 0}
We use the functional Itocalculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: lim inft→T Y (t) = ξ = Y (T )
It is already established that such a BSDE has a unique solution when the terminal condition ξ belongs to
Summary
We consider a filtered probability space ( , F, F, P) with a complete and right-continuous filtration F = {Ft , t ≥ 0}. We assume that this space supports a Brownian motion W. We consider the following BSDE: T. t t t where f is the generator and ξ is the terminal condition. The solution is the triplet (Y, Z , M). Since no particular assumption is made on the underlying filtration, there is the additional martingale part M orthogonal to W. It is already established that such a BSDE has a unique solution when the terminal condition ξ belongs to
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