In the course of our investigations of exponential Brownian functionals (Nagoya Math. J. 162 (2001) 65) we noticed, with the help of some previous work by Letac and Seshadri (Z. Wahr. verw. Geb. 62 (1983) 485), some identity in law involving GIG and gamma variables. In the present note, we give...

We present explicit formulae for the positive and negative moments of an exponential Wiener functional, which is defined as the integral with respect to time of geometric Brownian motion and plays an important role in several fields.

In this note, we show how to deduce some relationships between exponential functionals of Brownian motions with two different drifts from the case where the drifts are opposite from each other. We clarify which other properties than the Cameron-Martin relation are involved in proving these...

These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.

In this paper, we propose several "measurements" of the "non-stopping timeness" of ends g of previsible sets, such that g avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times of some remarkable martingales.

We introduce a class of stochastic processes, which we refer to as Lyrebirds. These extend a class of stochastic processes, which have recently been coined as Peacocks, but are more commonly known as processes which are increasing in the convex order. We show how these processes arise naturally...

We extend the Rothschild and Stiglitz (1970, 1971) notion of increasing risk to families of random variables and in this way link their approach to the concept of stochastic processes which are increasing in the convex order. These processes have been introduced in seminal work by Strassen...

We first discuss some mathematical tools used to compute the intensity of a single jump process, in its canonical filtration. In the second part, we try to clarify the meaning of default and the links between the default time, the asset?s filtration, and the intensity of the default time. We...