Abstract
In this paper we are concerned with one-dimensional backward stochastic differential equations (BSDE in short) of the following type:
Yt=ξ−∫t∧ττYr|Yr|q dr−∫t∧ττZr dBr, t≥0,
where τ is a stopping time, q is a positive constant and ξ is a ℱτ-measurable random variable such that P(ξ=+∞)>0. We study the link between these BSDE and the Dirichlet problem on a domain D⊂ℝd and with boundary condition g, with g=+∞ on a set of positive Lebesgue measure.
We also extend our results for more general BSDE.
Citation
A. Popier. "Backward stochastic differential equations with random stopping time and singular final condition." Ann. Probab. 35 (3) 1071 - 1117, May 2007. https://doi.org/10.1214/009117906000000746
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