Dr Jorge Gonzalez Cazares

Jorge is a Research Fellow at the Department of Statistics of the University of WarwickLink opens in a new window and a Visiting Researcher of the Mathematical FoundationsLink opens in a new window Challenge of the Programme on Data-Centric EngineeringLink opens in a new window at The Alan Turing InstituteLink opens in a new window.

Education

Jorge completed his Master's and Undergraduate degrees at the Faculty of SciencesLink opens in a new window of the National Autonomous University of MexicoLink opens in a new window in Mathematical Sciences and Actuarial Sciences, respectively.

Research Interests

Probability: invariance principles, local time, coupling, stochastic analysis for processes with and without jumps, Levy processes, exchangeable increment processes, random walks, Markov chains, optimal stopping.
Statistics: machine learning, parametric and non-parametric estimation.

Numerical stochastics: simulation of processes with and without jumps, weak and strong approximations, Monte Carlo, simulation.
Mathematical finance: risk management and price prediction, stochastic volatility models with jumps, arbitrage.

Articles

Title: Asymptotic shape of the concave majorant of a Lévy process
Authors: Bang, D., González Cázares, J.I., Mijatović, A.
To appear in Annales Henri Lebesgue (2022)
Links: arXiv

Title: Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation
Authors: González Cázares, J.I., Mijatović, A.
To appear in Finance and Stochastics (2022)
Links: arXiv, GitHub

Title: Geometrically Convergent Simulation of the Extrema of Lévy Processes
Authors: González Cázares, J.I., Mijatović, A., Uribe Bravo, G.
To appear in Mathematics of Operations Research (2021)
Links: arXivLink opens in a new window, GitHubLink opens in a new window

Title: Implementable coupling of Lévy process and Brownian motion
Authors: Fomichov, V., González Cázares, J.I., Ivanovs, J.
Stochastic Processes and Their Applications 142 (2021)
Links: MR4321329, arXiv

Title: Recovering Brownian and jump parts from high-frequency observations of a Lévy process
Authors: González Cázares, J.I., Ivanovs, J.
Bernoulli 27 (2021)
Links: MR4303889, arXivLink opens in a new window

Title: A Gaussian approximation theorem for Lévy processes
Authors: Bang, D., González Cázares, J.I., Mijatović, A.
Electronic Journal of Probabability 25 (2020)
Links: MR4285923, arXiv

Title: $epsilon squared$ -strong simulation of the convex minorants of stable processes and meanders
Authors: González Cázares, J.I., Mijatović, A., Uribe Bravo, G.
Electronic Journal of Probabability 25 (2020)
Links: MR4136476, arXiv, GitHub

Title: Exact Simulation of the Extrema of Stable Processes
Authors: González Cázares, J.I., Mijatović, A., Uribe Bravo, G.
Advances in Applied Probability, 51 (2019)
Links: MR4032169, arXivLink opens in a new window, GitHubLink opens in a new window

Preprints

Title: Convex minorants and the fluctuation theory of Lévy processes (2021)
Authors: González Cázares, J.I., Mijatović, A.
Links: arXiv

Title: Monte Carlo algorithm for the extrema of tempered stable processes (2021)
Authors: González Cázares, J.I., Mijatović, A.
Links: arXiv

Title: Joint density of a stable process and its supremum: regularity and upper bounds (2020)
Authors: González Cázares, J.I., Kohatsu-Higa, A., Mijatović, A.
Links: arXiv

Recent Presentations

Université de Lausanne. Actuarial seminar. May 2022
Isaac Newton Institute. Stochastic control and fractional dynamics. April 2022.
Ritsumeikan University. Probability seminar. 13th, 20th and 27th of June 2019 and 22th of April 2021.
National Autonomous University of Mexico. SPH seminar. 24th of May 2021
Bernoulli One World Symposium. August 2020
University of Warwick. Algorithms seminar. 31st of May 2019.
University of Kent. SMSAS seminar. 23rd of November 2018.

Contact Information

Emails: jorge dot ignacio dot gc at gmail dot com, Jorge dot I dot Gonzalez-Cazares at warwick dot ac dot uk or jgonzalezcazares at turing dot ac dot uk

ResearchGateLink opens in a new window, ORCiDLink opens in a new window, arXivLink opens in a new window, GitHubLink opens in a new window, The Alan Turing InstituteLink opens in a new window, Personal webpageLink opens in a new window

Short YouTube videos of some of the articles are availableLink opens in a new window.