11 citations · 61 across the 13 of their papers we have counts for
13 papers
Fast exact simulation of the first-passage event of a subordinator
Jorge Ignacio González Cázares, Feng Lin, Aleksandar Mijatović
This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-i…
Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function
Jorge Ignacio González Cázares, Feng Lin, Aleksandar Mijatović
We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non…
How smooth can the convex hull of a Lévy path be?
David Bang, Jorge González Cázares, Aleksandar Mijatović
We describe the rate of growth of the derivative of the convex minorant of a Lévy path at times where increases continuously. Since the convex minorant is piecewise linea…
Hölder continuity of the convex minorant of a Lévy process
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We characterise the Hölder continuity of the convex minorant of most Lévy processes. The proof is based on a novel connection between the path properties of the Lévy process at zer…
When is the convex hull of a Lévy path smooth?
David Bang, Jorge Ignacio González Cázares, Aleksandar Mijatović
We characterise, in terms of their transition laws, the class of one-dimensional Lévy processes whose graph has a continuously differentiable (planar) convex hull. We show that thi…
Asymptotic shape of the concave majorant of a Lévy process
David Bang, Jorge Ignacio González Cázares, Aleksandar Mijatović
We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value…
Convex minorants and the fluctuation theory of Lévy processes
Jorge Ignacio González Cázares, Aleksandar Mijatović
We establish a novel characterisation of the law of the convex minorant of any Lévy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex…
Implementable coupling of Lévy process and Brownian motion
Vladimir Fomichov, Jorge González Cázares, Jevgenijs Ivanovs
We provide a simple algorithm for construction of Brownian paths approximating those of a Lévy process on a finite time interval. It requires knowledge of the Lévy process trajecto…
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation
Jorge González Cázares, Aleksandar Mijatović
We develop a computational method for expected functionals of the drawdown and its duration in exponential Lévy models. It is based on a novel simulation algorithm for the joint la…
Recovering Brownian and jump parts from high-frequency observations of a Lévy process
Jorge González Cázares, Jevgenijs Ivanovs
We introduce two general non-parametric methods for recovering paths of the Brownian and jump components from high-frequency observations of a Lévy process. The first procedure rel…
-strong simulation of the convex minorants of stable processes and meanders
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
Using marked Dirichlet processes we characterise the law of the convex minorant of the meander for a certain class of Lévy processes, which includes subordinated stable and symmetr…
Geometrically Convergent Simulation of the Extrema of Lévy Processes
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
We develop a novel approximate simulation algorithm for the joint law of the position, the running supremum and the time of the supremum of a general Lévy process at an arbitrary f…
Exact Simulation of the Extrema of Stable Processes
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpe…