We present a general model for default times, making precise the role of the intensity process, and showing that this process allows for a knowledge of the conditional distribution of the default only "before the default". This lack of information is crucial while working in a multi-default...

We infer in this paper a rather general probabilistic stochastic control method for some problems occurring in parametrical statistics, illustrated by two examples of accelerated life testing.

Wolfe (Stochastic Process. Appl. 12(3) (1982) 301) and Sato (Probab. Theory Related Fields 89(3) (1991) 285) gave two different representations of a random variable X1 with a self-decomposable distribution in terms of processes with independent increments. This paper shows how either of these...

Résumé On étudie par des méthodes de type calcul stochastique les propriétés de martingales d'une classe très générale de processus de branchement à valeurs mesures. Leurs caractéristiques locales et temps d'explosion sont explicités en fonction de la forme de leur cumulant. Enfin,...

For a given filtered probability space , an -adapted continuous increasing process [Lambda] and a positive - local martingale N such that [Lambda]0=0 and Nte-[Lambda]t=1, we construct a probability measure and a random time [tau] such that and . The probability is linked with the well-known Cox...

The preservation of the semi-martingale property in progressive enlargement of filtrations has been studied by many authors. Most of them focus on progressive enlargement with a honest time, allowing for semi-martingale invariance and simple decomposition formulas. However, times allowing for...

Given a filtered probability space , an -adapted continuous increasing process [Lambda] and a positive local martingale N such that satisfies Zt<=1,t>=0, we construct probability measures and a random time [tau] on an extension of , such that the survival probability of [tau], i.e., is equal to Zt for...</=1,t>

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time τ. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in...