About Me

Who Am I?

Hi!! I'm Jonathan Chávez Casillas. I am an Assistant Professor of Mathematics at the University of Rhode Island. My main interests lie in Probability Theory and Stochastic Processes, particulary in their usage for modeling and applications to Mathematical Finance, Epidemiology and Marine Ecology.

I am also interested in Actuarial Sciences and I have successfully completed some of the examinations of the Socitey of Actuaries and I am teaching some of their related coursework.

Probability
and
Stochastic Processes

Stochastic Modelling and Stochastic Optimization

Mathematical Finance and Actuarial Sciences

Marine Ecology as a Field of Application for Data Science

I have also taught more than 10 different college courses looking always to innovate in the classes I teach as well as to consolitdate the knowledge they have acquired up to that point in their education.

My Current Research Interests and Areas of Applications are Listed Below

Research Interests and Publications

Stochastic Processes

Theoretical Probability Theory from the perspective of Mathematical Analysis

Stochastic Processes

Theory, Convergence, and Fluid Dynamics Analysis of Random Processes

Point Processes

Intensity based Point Processes: Statistical Properties and Applications

Mathematical Finance

High Frequency Markets, Limit Order Book modelling and Stochastic Optimization problems related to them

Mathematical Biology

Modelling of Population Dynamics, particulary in Epidemiology and related areas

Marine Ecology

Applications of Data Science and Data Analysis in problems related to Marine Ecology


Publications

Below, you can find my publications.

Current Work and Preprints

Below, you can find some of my current work and some preprints.

A Stochastic Model for the Early Stages of Highly Contagious Epidemics by using a State-Dependent Point Process

Link
Download

Adaptive Optimal Market Making Strategies with Inventory Liquidation Cost

Joint work with
  • José E. Figueroa-López
  • Chuyi Yu
  • Yi Zhang

Log-transformations of probability distributions in clinical sciences

Joint work with
  • Joshua Tanzer
Courses I am Teaching and have previously taught

Teaching

Below, you can find the list of courses I have taught at URI and the percentage of times I have taught them.


Current Semester: Spring 2023


Current Teaching Load: MTH 106, AMS/DSP 393G and MTH 451


Total number of courses taught since my arrival at URI: 45


MTH 106: Mathematics of Social Choice and Finance


Textbook: Math in Society by David Lippman


27%

MTH 215: Introduction to Linear Algebra


Textbook: Linear Algebra with applications by Keith Nicholson


11%

MTH 362: Advanced Engineering Mathematics


Textbook: Advanced Engineering Mathematics, 10th Edition by Erwin Kreyszig


7%

AMS/DSP 393G: Introduction to Predictive Analytics


Textbook: Regression modeling with actuarial and financial applications by Edward W. Frees


7%

MTH 451: Introduction to Probability and Statistics


Textbook: Probability and Mathematical Statistics by Mary C. Meyer


16%

MTH 452: Mathematical Statistics


Textbook: Probability and Mathematical Statistics by Mary C. Meyer


5%

MTH 453: Basic Random Processes


Textbook: Introduction to Stochastic Processes With R by Robert P. Dobrow


5%

MTH 471: Introduction to Numerical Analysis


Textbook: Numerical Analysis: Mathematics of Scientific Computing by Kincaid and Cheney


2%

MTH 552: Mathematical Statistics


Textbook: Probability and Mathematical Statistics by Mary C. Meyer


5%

MTH 591/592: Special Problems


Textbook: Various


5%
Education

Below you can find my educational background.

Year granted: 2015

Course based MSc degree with emphasis on Derivative Pricing, Hedging, Valuation, Continuous Time Arbitrage theory and Stochastic Calculus for Finance.

Advisor: Dr. Esteban A. Chávez Casillas

Year granted: 2009

Thesis: Solutions of Second Order Elliptical PDEs in High Dimensions using Monte Carlo Methods.

Experience

Work Experience

Assistant Professor of Mathematics at URI 2017-Present

  • Performing research in Mathematical Finance, Epidemiology and, recently, in Marine Ecology.
  • Have taught multiple courses at the undergraduate and graduate level.
  • Have advised students at the undergraduate and graduate level.

PIMS postdoctoral scholar in Stochastics at UCalgary 2015-2017

  • Performed research in Mathematical Finance, High-Frequency trading models and Semi-Markov Processes.
  • Taught multiple courses at the undergraduate level.

PhD student and Teaching Assitant at Purdue University 2009-2015

  • Performed research in Mathematical Finance, High-Frequency trading models and Stochastic Analysis.
  • Taught multiple courses at the undergraduate level.

Here you can find my CV.


Last Updated:

January 2023

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Get in Touch

Contact

5 Lippit Road, Suite 200A, Kingston RI 02882