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

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  • Cacitti-Holland, Dorian
  • Denis, Laurent
  • Popier, Alexandre

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.

Suggested Citation

  • Cacitti-Holland, Dorian & Denis, Laurent & Popier, Alexandre, 2025. "Growth condition on the generator of BSDE with singular terminal value ensuring continuity up to terminal time," Stochastic Processes and their Applications, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:spapps:v:183:y:2025:i:c:s0304414925000298
    DOI: 10.1016/j.spa.2025.104588
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