Jorge Gonzalez Cazares

Jorge is a fourth-year PhD student at the Department of Statistics of the University of Warwick under the supervision of Prof. Aleksandar Mijatović. Jorge is a Visiting Researcher of the Mathematical Foundations Challenge of the Programme on Data-Centric Engineering at The Alan Turing Institute.

Education

Jorge completed his Master's and Undergraduate degrees at the Faculty of Sciences of the National Autonomous University of Mexico 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: Exact Simulation of the Extrema of Stable Processes (2018)

Authors: González Cázares, J.I., Mijatović, A., Uribe Bravo, G.

Advances in Applied Probability, 51(4) (December 2019)

Links: arXiv, GitHub

Title: Geometrically Convergent Simulation of the Extrema of Lévy Processes (2018)

Authors: González Cázares, J.I., Mijatović, A., Uribe Bravo, G.

To appear in Mathematics of Operations Research

Links: arXiv, GitHub

Title: $epsilon squared$ -strong simulation of the convex minorants of stable processes and meanders (2019)
Authors: González Cázares, J.I., Mijatović, A., Uribe Bravo, G.
Electronic Journal of Probabability 25 (2020)
Links: arXiv, GitHub

Preprints

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

Title: A Gaussian approximation theorem for Lévy processes (2021)
Authors: González Cázares, J.I., Mijatović, A., Bang, D.
Links: arXiv

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

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

Title: Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation (2020)
Authors: González Cázares, J.I., Mijatović, A.
Links: arXiv, GitHub

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

Title: Recovering Brownian and jump parts from high-frequency observations of a Lévy process (2020)
Authors: González Cázares, J.I., Ivanovs, J.
Links: arXiv

Recent Presentations

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 Gonzalez-Cazares at warwick dot ac dot uk or jgonzalezcazares at turing dot ac dot uk

ResearchGate, ORCiD, arXiv, GitHub, The Alan Turing Institute, Personal webpage

Short YouTube videos of some of the articles are available.