Academic portfolio · Puebla, Mexico
Actuarial Science and Data Science student at Universidad de las Américas Puebla.
I work across stochastic geometry, probability, time series, financial risk, and interpretable machine learning. My projects combine mathematical modeling, reproducible computation, and applied data analysis.
Selected papers
Research in stochastic geometry and empty-region proximity graphs.
Selected manuscripts under review and research projects; see the full archive for all paper records and materials.
Manuscript A fixed-template empty-region rule assigns a Borel region \(S(p,q)\) to a candidate pair and retains the edge when that region contains no other site. The manuscript isolates the unit-volume constant \(a_K\) for similarity-copy regions and shows how the same scalar controls exact Poisson void probabilities, incident-edge length intensities, mean out-degree, and normalized incident-edge length laws.
Manuscript This manuscript develops a geometric, graph-theoretic, and probabilistic analysis of the stepping-stone graph in \(\mathbb{R}^d\) for every \(d\geq 2\). It derives a normalized one-dimensional volume integral, recovers the degenerate and Gabriel cases and the relative-neighborhood limit, proves strict region and volume monotonicity, establishes graph inclusions and connectivity, and validates a stable quadrature formula by rejection sampling.
Selected projects
Research software for proximity graphs, quantitative finance, and computational geometry.
Selected research and software projects; see the full archive for every project and its materials.
Applied / software Proximity Graphs is a Python library for generating and manipulating point sets, creating geometric and proximity graphs, analyzing graph properties, and visualizing graphs and point patterns.
Applied / software AbaQuant is an applied actuarial and quantitative-finance Python library covering pricing models, financial mathematics, market data, credit analytics, portfolio construction, rate curves, visualizations, exportable reports, and provenance-aware result objects.
Selected academic projects
Course projects in actuarial modeling, quantitative finance, econometrics, and data analysis.
Selected academic and course projects are shown here; visit LinkedIn for certifications, awards, and additional academic activity.
Course project Bayesian valuation study for Asian options using Metropolis–Hastings inference for geometric-Brownian-motion parameters and posterior simulation to propagate parameter uncertainty into option values.
Course project A computational laboratory for systemic liquidity stress. The model connects heterogeneous market participants, stochastic shocks, margin constraints, forced liquidation, stress metrics, and network fragmentation without fixing a public market description that remains under review.
Selected posters & presentations
Visual academic materials from project work.
Selected visual academic materials are shown here; see the archive for all available posters and presentations.
Course project Poster project proposing a latent financial-risk index from representative global signals such as implied volatility, oil, gold, and the dollar index. The workflow combines dynamic factor modeling with penalized least-squares smoothing and Guerrero-style smoothness selection through validation.
Academic presentation Academic presentation connecting local geometric acceptance rules in proximity graphs with global probabilistic laws, using nearest-neighbor, Gabriel, relative-neighborhood, and Delaunay graphs as motivating examples.
Notes
Mathematical notes developed through independent study and research preparation.
All currently available mathematical notes are shown here and maintained in the notes archive.
Study notes In-progress notes formalizing random variables as vectors in the Hilbert space \(L^2(\Omega,\mathcal{F},\mathbb{P})\). They interpret expectation and conditional expectation as orthogonal projections, variance and bias-variance as Pythagorean decompositions, and Chapman-Kolmogorov as a tower-property identity.
