Leonardo Medina

Leonardo Medina Espinosa, M.Sc.
Master’s in Mathematics with a specialization in Probabilities (Pontificia Universidad Católica de Chile, PUC)
Mathematician (Escuela Politécnica Nacional, EPN)

Profile
I am a researcher and professor specialized in stochastic processes, probability theory, simulation, risk models, and statistics, with a solid theoretical background and experience in interdisciplinary applications. My work spans from fundamental problems in probability—such as random walks, random environments, and multiplicative chaos—to applied developments in finance, insurance, data science, and predictive analytics.

I have participated in innovative projects that combine mathematical theory with computational implementation, and I enjoy developing solutions and products that connect advanced probabilistic models with real-world needs. Furthermore, I have experience in teaching at different levels, academic leadership, and coordinating student support programs.

Areas of Expertise

• Stochastic Processes
• Probability Theory
• Risk Models and Actuarial Mathematics
• Stochastic Simulation
• Bayesian and Classical Statistics
• Probabilistic Modeling with applications in Finance and Insurance
• Numerical Methods and Functional Analysis
• Scientific Computing and Data Analysis (Python, R)

Selected Publications

• Medina Espinosa (2023). Directed Polymers in Complex-Valued Random Environments. arXiv:2310.02209.
• Medina Espinosa (2023). Limit laws for hitting times of random walks with slowly varying tails. Springer Proceedings in Mathematics & Statistics. https://doi.org/10.1007/s12591-023-00638-x
• Medina Espinosa (2021). A remark on recurrence and transience criteria for one-dimensional random walks in random environments. Bulletin of the Korean Mathematical Society. https://doi.org/10.4134/BKMS.b210307

Teaching Experience

• Stochastic Processes for Finance and Insurance — Master’s in Actuarial Science, EPN–PUCE.
• Risk Models and Simulation — Undergraduate Program in Mathematics, EPN.
• Applied Statistics — Undergraduate Program in Statistics, PUC.
• Mathematical Economics — Graduate Program in Economics, PUC.
• Calculus, Linear Algebra, Probability and Statistics — Undergraduate Program in Engineering, EPN.
• Linear Algebra, Probability and Statistics, Fundamentals of Mathematics — Undergraduate Program in Sciences, Yachay Tech.
• Business Mathematics, Mathematical Reasoning — Undergraduate Program in Sciences, USFQ.
• Academic Coordinator of CLAVEMAT-EPN, leading a team of ~70 tutors and achieving a 20% reduction in student dropout rates through inclusive strategies.

Talks and Academic Activities

• Organization of student seminars in probability, statistics, and simulation (EPN).
• Lectures delivered:
  • Random walks in random environments with heavy tails, Escuela Nacional de Optimización, UNAM (Mexico).
  • Probability models for financial risk, internal conference series, PUC (Chile).
  • Stochastic models and simulation, student seminars, EPN (Ecuador).
• Participation in international summer schools on probability, stochastic processes, and simulation.
• Mentor for students in research projects and academic presentations.

Projects and Collaborations

• Winner of the SinLímites 2022 Program (Entel): development of predictive models for user behavior, machine learning, and data analytics.
• Academic collaborations with research groups in Chile and Mexico, including the Escuela Nacional de Optimización (UNAM).
• Participation in international conferences and workshops on probability, simulation, and numerical methods.