Modelling general default times under risk neutral probability

Session 5: Risk Modelling and Machine Learning

Abstract: It is known that, starting from a reference filtration F, to construct an arbitrage free model with default in the enlarged filtration G, immersion has to hold under a risk neutral probability. This implies that, under this risk neutral probability Q, the survival conditional law Q(τ > t|Ft) of the default is decreasing. This enables us to construct in a general way default times, in particular ones which do not avoid a given sequence of F-stopping times.
(Based on joint work with D. Gueye)