First-passage times (FPTs) of two-dimensional Brownian motion have many applications in
quantitative finance. However, despite various attempts since the 1960s, there are few …

From both theoretical and applied perspectives, first passage time problems for random
processes are challenging and of great interest. In this thesis, our contribution consists on …

The distribution of the α-quantile of a Brownian motion on an interval [0, t] has been obtained
motivated by a problem in financial mathematics. In this paper we generalize these results …

Let τr denote the hitting time of B (0: r) for a multidimensional diffusion process. We give
verifiable criteria for finiteness/infiniteness of As an application we exhibit classes of …

The drawdown process of a one-dimensional regular diffusion process X is given by X
reflected at its running maximum. The drawup process is given by X reflected at its running …

The Law of Geometric Brownian Motion and its Integral, Revisited Application to Conditional
Moments Page 1 The Law of Geometric Brownian Motion and its Integral, Revisited …

The probability of a Brownian motion with drift to remain between two constant barriers (for
some period of time) is known explicitly. In mathematical finance, this and related results are …

Let={≧ 0} be a one-dimensional standard Brownian motion starting from 0. To (µ)={(µ)=+
µ≧ 0}, a Brownian motion with constant drift µ, we associate the exponential additive …

A continuous time random walk (CTRW) is a random walk subordinated to a renewal
process, used in physics to model anomalous diffusion. Transition densities of CTRW …

An alternative expression for the Black-Scholes formula in terms of Brownian first and last
passage times Page 1 HAL Id: hal-00257403 https://hal.science/hal-00257403 Preprint …