Blog
This is my personal blog. It showcases applied mathematics across a wide span of subjects, from physics and engineering to finance, history and medicine: the models, the methods that solve them, the code that runs them and the algorithms behind them, often with a live model you can try for yourself. Each post starts from a question and works it through to a number. Nothing here is a product or advice; the research papers live under Research.
Two Worlds, One Price: Entropy and the Risk-Neutral Measure
The change of measure at the heart of derivative pricing is an exponential tilt of the real-world probability measure — identical in structure to the Boltzmann distribution. The cost of that tilt is relative entropy.
Read more →Pricing a Gas Liquefaction Plant as a Real Option: An HJB Approach
We price the option to invest in a gas liquefaction plant using the Hamilton-Jacobi-Bellman PDE, with CIR gas price dynamics and a finite-horizon free boundary problem.
Read more →Heat Diffusion in an Iron Sphere — A FEniCSx Simulation
A 3D FEniCSx simulation of heat diffusing through an iron sphere with a hot core. Full PDE, boundary conditions, weak form, and DOLFINx code.
Read more →Solar Magnetohydrodynamics: Solving Magnetic Diffusion in a Sphere
Solving the MHD induction equation in spherical geometry with Dedalus — magnetic diffusion on the 2D sphere surface and inside a 3D conducting ball, with animated GIF simulations.
Read more →Solving the 2D Wave Equation with Spectral Methods
Using the Dedalus spectral PDE solver to simulate the 2D wave equation on a periodic domain, with animated GIF output and applications across physics, finance, and medical imaging.
Read more →The Square Root That Keeps Rain Positive: CIR Processes in Weather Modelling
The Cox-Ingersoll-Ross process was built for interest rates. Its real strength — staying positive as noise vanishes near zero — turns out to be exactly what rainfall modelling needs.
Read more →When Neurons Forget: The Ornstein-Uhlenbeck Process in Neuroscience
The leaky integrate-and-fire neuron — the workhorse model of computational neuroscience — is an Ornstein-Uhlenbeck process in disguise. Here is why that matters.
Read more →What Agent-Based Models See That Regressions Miss
Standard regression conflates micro configurations that produce identical macro observables. Four classical examples — wealth concentration from random exchange, Schelling segregation, phantom traffic jams, and bank runs — show that genuine causal structure can be invisible to aggregate statistics and only visible at the level of agent interactions.
Read more →The Mean Field Game of Mediocrity
Mean field game theory gives mediocracy a precise formulation: when conformity pressure exceeds rank incentive, the coupled HJB–Fokker–Planck system has a concentrated Nash equilibrium. A phase transition separates dispersed outcomes from universal indistinction.
Read more →Agent-Based Models in the Peanut Butter Industry
Any market with heterogeneous agents, inventory dynamics, and competitive pricing produces emergent behavior that ABM is built to capture. Peanut butter turns out to be a surprisingly clean example.
Read more →ABM or MFG? The Cases Where the Answer Is Not Clear
Agent-based models and mean field games are often presented as alternatives. In practice, a significant share of real problems sit between them — and recognizing that grey zone is the first step toward modeling it correctly.
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