This text is a survey of the general theory of stochastic processes, with a view towards
random times and enlargements of filtrations. The first five chapters present standard …

In the theory of progressive enlargements of filtrations, the supermartingale $ Z_ {t}=\mathbf
{P}(g> t\mid\mathcal {F} _ {t}) $ associated with an honest time $ g $, and its additive (Doob …

This paper studies drawdown and drawup processes in a general diffusion model. The main
result is a formula for the joint distribution of the running minimum and the running maximum …

In this paper we examine the probabilistic behavior of two quantities closely related to
market crashes. The first is the drawdown of an asset and the second is the duration of time …

We propose a general framework for studying last passage times, suprema, and drawdowns
of a large class of continuous-time stochastic processes. Our approach is based on …

This paper consists of two independent parts. In the first one, we contribute to the study of
the class. For instance, we provide a new way to characterize stochastic processes of this …

We characterize the set W of possible joint laws of terminal values of a nonnegative
submartingale X of class (D), starting at 0, and the predictable increasing process …

Abstract A single jump filtration ${({\mathcal {F} _ {t}}) _ {t\in {\mathbb {R} _ {+}}}} $ generated
by a random variable γ with values in ${\overline {\mathbb {R}} _ {+}} $ on a probability …

This paper contributes to the study of stochastic processes of the class (Σ)(Σ). First, we
extend the notion of the above-mentioned class to càdlàg semi-martingales, whose finite …

In this survey on last passage times, we propose a new viewpoint which provides a unified
approach to many different results which appear in the mathematical finance literature and …