Backward stochastic differential equations with random stopping time and singular final condition

• 成果类型: Article
• 署名作者: Popier, A.
• 署名单位: Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000746
• 发表日期: 2007
• 页码: 1071-1117
• 关键词: positive solutions; BOUNDARY; trace

摘要

In this paper. we are concerned with one-dimensional backward stochastic differential equations (BSDE in short) of the following type: Y-t = xi - integral(tau)(t Lambda tau) Y-r vertical bar Y-r vertical bar(q) dr - integral(tau)(t Lambda tau) Z(r) d B-r, t >= 0, where tau is a stopping time, q is a positive constant and xi is a F-tau-measurable random variable such that P(xi = +infinity) > 0. We study the link between these BSDE and the Dirichlet problem on a domain D subset of R-d and with boundary condition g, with g = +infinity on a set of positive Lebesgue measure. We also extend our results for more general BSDE.