Growth condition on the generator of BSDE with singular terminal value ensuring continuity up to terminal time

Dorian Cacitti-Holland, Laurent Denis and Alexandre Popier

Stochastic Processes and their Applications, 2025, vol. 183, issue C

Abstract: We study the limit behavior of the solution of a backward stochastic differential equation when the terminal condition is singular, that is it can be equal to infinity with a positive probability. In the Markovian setting, Malliavin’s calculus enables us to prove continuity if a balance condition between the growth w.r.t. y and the growth w.r.t. z of the generator is satisfied. As far as we know, this condition is new. We apply our result to liquidity problem in finance and to the solution of some semi-linear partial differential equation ; the imposed assumption is also new in the literature on PDE.

Keywords: Backward stochastic differential equation; Singular terminal condition; Malliavin’s calculus (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104588

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