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Dr Jorge Gonzalez Cazares

Jorge is a postdoctoral researcher 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.