Research Progress
In progressAmerican Option Pricing: Free Boundary Method
Notes on the numerical approximation of the early exercise boundary of American options using PDE-based free boundary formulations.
Nonlinear Black–Scholes: Full-Feedback PDE
Exploration of the Glover–Duck–Newton full-feedback model and comparison with the classical Black–Scholes framework.
Numerical Methods
Study notesFinite Difference Methods for Parabolic PDEs
Derivation and analysis of Crank–Nicolson, θ-methods, and higher-order schemes for parabolic equations.
Penalty Methods for Free Boundary Problems
Overview of penalty and complementarity formulations for free boundary problems arising in option pricing.
Mathematics
Study notesFunctional Analysis — Selected Topics
Notes on Banach and Hilbert spaces, bounded linear operators, spectral theory, and applications to PDE analysis.
Probability & Stochastic Calculus
Measure-theoretic probability, Brownian motion, Itô's lemma, and the Feynman–Kac formula.
Machine Learning
Study notesEach note links to a dedicated page. Notes marked In Progress are actively being written; Draft notes exist but are not yet fully polished.