Research interests
My main interests are in probability theory, stochastic processes, and mathematical analysis. I am particularly interested in quantitative approximation problems, probability metrics, controlled Markov processes, and the analysis of stochastic and deterministic models.
During my graduate studies, I expect to deepen my background in probability and analysis and to explore problems where these areas interact.
Previous research
My previous work has been carried out mainly in collaboration with Dr. Evgueni Gordienko at Universidad Autónoma Metropolitana.
A central theme of this work has been the quantitative comparison of mathematical models: In optimization settings, it is often difficult or even impossible to find exact solutions to a given problem. Meanwhile, it can be easier to find solutions to a simplified problem. We want to know how much accuracy we lose by using the solution of the simpler problem as a replacement for the original one.
In particular, we have studied the optimization of a portfolio investment model described as a controlled discrete-time Markov process. Using probability metrics and stability estimates, we gave an upper bound for the loss in the total discounted utility when replacing the (random) returns of risky assets with their (deterministic) mean.
We have did similar work in the comparison between (sometimes complicated) differential models of population growth and their approximation by the (usually simpler) logistic model, giving upper bounds for the maximum deviation between the two models over finite and infinite time intervals.
This work has resulted in joint publications and an international conference presentation.
Earlier work
As an undergraduate, I also completed a research project in abstract algebra, focused on injective and projective modules and their categorical characterizations. This project resulted in a written report and two presentations.
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