185 citations · 202 across the 10 of their papers we have counts for
13 papers
Boundary crossing problems and functional transformations for Ornstein-Uhlenbeck processes
Aria Ahari, Larbi Alili, Massimiliano Tamborrino
We are interested in the law of the first passage time of an Ornstein-Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first…
A comparison of European and Asian options under Markov additive processes
David Woodford, Larbi Alili
We provide results relating to the integrability, uniform integrability and local integrability of exponential MAPs, which are natural extensions of exponential Levy models. Then,…
On Doney's striking factorization of the arc-sine law
Larbi Alili, Carine Bartholmé, Loïc Chaumont +3
R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximat…
On finiteness and tails of perpetuities under a Lamperti-Kiu MAP
Larbi Alili, David Woodford
Consider a Lamperti-Kiu Markov additive process on where is the modulating Markov chain component. First, we study the fi…
Further studies on square-root boundaries for Bessel processes
Larbi Alili, Hiroyuki Matsumoto
We look at decompositions of perpetuities and apply that to the study of the distributions of hitting times of Bessel processes of two types of square root boundaries. These distri…
Space and time inversions of stochastic processes and Kelvin transform
Larbi Alili, Loïc Chaumont, Piotr Graczyk +1
Let be a standard Markov process. We prove that a space inversion property of implies the existence of a Kelvin transform of -harmonic, excessive and operator-harmonic f…