School of Mathematical Sciences
Faculty of Sciences, Engineering and Technology
Eligible to supervise Masters and PhD (as Co-Supervisor) - email supervisor to discuss availability.
I am a mathematician with an interest in the foundations and modeling of random phenomena. I studied my BSc in Actuarial Sciences and MSc in Mathematics at the National Autonomous University of México. Later on, I obtained my PhD in Applied Mathematics in 2019 from the Technical University of Denmark. From September 2018 to November 2021 I worked as an ARC Research Associate at The University of Adelaide - currently I holding an Adjunct Lecturer position - working with Dr. Giang T. Nguyen . In December 2021 I became a SNSF Senior Researcher at the University of Lausanne (Switzerland), working with Prof. Hansjoerg Albrecher.
My interests lie in the area of probability and stochastic processes (applied and theoretical).
Recent projects include:
- Strong convergence of stochastic processes
- Stochastic differential equations in regime-switching environments
- Phase-type distributions and dependence in risk theory
Date Position Institution name 2021 - ongoing Adjunct Lecturer The University of Adelaide 2021 - ongoing SNSF Senior Researcher University of Lausanne 2018 - 2021 ARC Research Associate The University of Adelaide 2015 - 2018 Research Assistant Technical University of Denmark
Language Competency Spanish - Latin American Can read, write, speak, understand spoken and peer review
Date Institution name Country Title 2015 - 2019 Technical University of Denmark Denmark PhD in Applied Mathematics 2013 - 2014 National Autonomous University of Mexico Mexico MSc in Mathematics 2008 - 2012 National Autonomous University of Mexico Mexico BSc in Actuarial Sciences
Year Citation 2022 Nguyen, G. T., & Peralta, O. (2022). Rate of strong convergence to Markov-modulated Brownian motion. Journal of Applied Probability, 59(1), 1-16.
2020 Nguyen, G. T., & Peralta, O. (2020). An explicit solution to the Skorokhod embedding problem for double exponential increments. Statistics and Probability Letters, 165, 5 pages.
2019 Bladt, M., Nielsen, B. F., & Peralta, O. (2019). Parisian types of ruin probabilities for a class of dependent risk-reserve processes. Scandinavian Actuarial Journal, 2019(1), 32-61.
2018 Peralta Gutierrez, O., Rojas-Nandayapa, L., Xie, W., & Yao, H. (2018). Approximation of ruin probabilities via Erlangized scale mixtures. Insurance: Mathematics and Economics, 78, 136-156.
During my PhD studies from 2015 to 2018, my scholarship was funded by the National Council of Science and Technology of México (CONACYT)
I have 7 years of experience as a Teaching Assistant of theoretical probability courses at BSc and MSc level in México and Denmark. In 2020, I was the course coordinator and lecturer of the course Applied Probability at The University of Adelaide.
Current Higher Degree by Research Supervision (University of Adelaide)
Date Role Research Topic Program Degree Type Student Load Student Name 2021 Co-Supervisor Diffusion Approximations for Epidemic Modelling and Correlated Pseudo-Marginal Inference Methods. Master of Philosophy Master Part Time Mr Michael Fairbrother 2021 Co-Supervisor Option pricing using Levy Processes observed at Poisson times Master of Philosophy Master Full Time Mr Jesse Benjamin Tonkin 2021 Co-Supervisor Strong solutions to Hybrid Stochastic Differential Equations with Past-Dependent Switching Master of Philosophy Master Full Time Mr William Allan 2021 Co-Supervisor Pathwise Convergence of Regime-Switching Stochastic Differential Equations via Rough Path Theory Doctor of Philosophy Doctorate Full Time Mr Jasper Barr 2020 Co-Supervisor Strong Convergence to Markov Modulated Fractional Brownian Motion Master of Philosophy Master Part Time Mr William Peter Abbott
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