Abstract : We consider a non-Markovian optimal stopping problem on finite horizon.
We prove that the value process can be represented by means of
a backward stochastic differential equation (BSDE), defined on an enlarged
probability space, containing a stochastic integral
one-jump point process as integrator
and an (unknown) process with a sign constraint as integrand.
This provides an alternative representation with respect to the classical
one given by a reflected BSDE. The connection between the two BSDEs
is also clarified. Finally, we prove that the value of the optimal
stopping problem is the same as the value of an auxiliary
optimization problem where the intensity of
the point process is controlled.