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Jorge Gonzalez Cazares

Jorge is a fourth-year PhD student at the Department of Statistics of the University of WarwickLink opens in a new window under the supervision of Prof. Aleksandar MijatovićLink opens in a new window. Jorge is 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: 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)

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: arXivLink opens in a new window, GitHubLink opens in a new window

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.ignacio.gc@gmail.com, Jorge.Gonzalez-Cazares@warwick.ac.uk or jgonzalezcazares@turing.ac.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.

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