  In this paper, we show that the minimal solution of a backward stochastic
differential equation gives a probabilistic representation of the minimal
viscosity solution of an integro-partial differential equation both with a
singular terminal condition. Singularity means that at the final time, the
value of the solution can be equal to infinity. Different types of regularity
of this viscosity solution are investigated: Sobolev, H{\"o}lder or strong
regularity.
