Appears in collection : A Random Walk in the Land of Stochastic Analysis and Numerical Probability / Une marche aléatoire dans l'analyse stochastique et les probabilités numériques

The Cox Construction of a totally inaccessible stopping time with a given compensator is ubiquitous in Mathematical Finance, and in particular in Credit Risk. On the other hand, as P.A. Meyer showed long ago, totally inaccessible stopping times arise naturally as the jump times of a strong Markov process. We relate the two ideas and propose a solution to a question posed by Monique Jeanblanc.