Research Assistants

Undergraduate student at the School of Mathematical and Computational Sciences at Yachay Tech University, focusing on pure and applied mathematics, particularly functional analysis, spectral theory, and the calculus of variations. His thesis research examines normalized ground-state solutions for nonlinear elliptic systems, drawing on Sobolev spaces, nonlinear analysis, and variational methods.

He also collaborates with MSc. Leonardo Medina, on developing educational resources, including solution manuals for Functional Analysis. As a Calculus Teaching Assistant, he is dedicated to supporting undergraduate students and enhancing the academic community.

An undergraduate Mathematics student at Yachay Tech University, Ecuador, he specializes in probability theory, stochastic processes, and mathematical finance. His thesis extends the discrete-time Cox–Ross–Rubinstein model to an incomplete market with three potential asset values at each time step, exploring moment-generating functions and exponential minimization for characterizing arbitrage-free models and risk-neutral measures. Combining probabilistic and analytical techniques, he examines the structure of financial markets and the pricing of derivatives under incompleteness. Additionally, he collaborates with MSc. Leonardo Medina teaches "Introduction to Stochastic Processes applied to Finance" and develops academic resources in probability and related areas, further enhancing his skills through advanced coursework and independent study.

This academic initiative focuses on the analysis and modeling of random phenomena within the financial and actuarial domains. It offers a hands-on approach to studying probabilistic models, aimed at enhancing decision-making and problem-solving abilities in situations characterized by high uncertainty.

A mathematics student at Yachay Tech University in Ecuador, he focuses on probability theory, stochastic processes, and control theory, particularly Poisson and Cox processes. His thesis examines optimal stop times in finance, integrating research on dynamical systems and the relationship between differential equations and time-scale analysis. He aims to unify continuous and discrete mathematical frameworks and apply these concepts to stochastic modeling. He has enhanced his skills in mathematical modeling, numerical computation, and scientific programming in Python and R, while contributing to projects such as Math2Braille. His academic journey is enriched by advanced coursework in functional analysis, topology, and differential equations, with a keen interest in exploring applications in stochastic processes and control theory.

Currently an undergraduate student in the School of Mathematical and Computational Sciences at Yachay Tech University, I specialize in both pure and applied mathematics, with a particular emphasis on probability theory, stochastic processes, and functional analysis. My thesis research delves into the coupon collector's problem, integrating analytical insights into expected waiting times and asymptotic behavior with Monte Carlo simulation studies conducted in R.

In addition to my academic pursuits, I co-taught "Introducción al cálculo para las finanzas." I served as a Calculus Teaching Assistant, where I am committed to supporting my fellow undergraduate students and fostering a vibrant academic community. Beyond mathematics, I am a passionate soccer player and continue to play regularly.