Backward stochastic differential equations with singular terminal condition

In this paper, we are concerned with backward stochastic differential equations (BSDE for short) of the following type: Yt=ξ−∫tTYr|Yr|qdr−∫tTZrdBr, where qq is a positive constant and ξξ is a random variable such that P(ξ=+∞)>0P(ξ=+∞)>0. We study the link between these BSDE and the associated Cauchy problem with terminal data gg, where g=+∞g=+∞ on a set of positive Lebesgue measure.