Writings

Essays and notes on finance, economics, data and intelligent systems.

ESSAY · QUANTITATIVEDraft

The binomial roots of Black–Scholes

ESSAY · TECHNICALDraft

Regimes, attractors and metastability

ESSAY · TECHNICALDraft

Reversing diffusion

ESSAY · ECONOMICDraft

Investment without productivity? The Moroccan growth model

Essays

TECHNICALDraft

Ergodicity: time averages and ensemble averages

On the conditions under which observations across time and observations across realizations can carry equivalent statistical information.

Time Series · Probability · Econometrics · Ergodicity

TECHNICALDraft

Two kinds of limits: from averages to extremes

A comparison between the limiting behavior of averages and the limiting behavior of extremes, from the central limit theorem to extreme value theory.

Probability · Statistics · Extreme Value Theory · Risk

TECHNICALDraft

Depth, composition and representation

Why depth remains useful when shallow neural networks are already universal approximators, and what composition changes about representation.

Neural Networks · Deep Learning · Approximation Theory · Representation Learning

TECHNICALDraft

The cost of moving data

On why memory access and data movement can become more important bottlenecks than arithmetic throughput in modern AI workloads.

GPU Computing · AI Systems · Memory · Performance Engineering · Parallel Computing

Notes

TECHNICALDraft

Gaussian noise in diffusion models

Diffusion Models · Probability · Gaussian Distribution · Generative AI

TECHNICALDraft

Ray: tasks, actors and distributed execution

Ray · Distributed Computing · ML Systems · Python

References

Advances in Financial Machine Learning

Marcos Lopez de Prado2018

All of Statistics

Wasserman2004

The Elements of Statistical Learning

Hastie2009

Time Series Analysis

Hamilton1994

Forecasting

Hyndman2021

Quantitative Risk Management

McNeil2015

The Volatility Surface

Gatheral & Taleb2006

Stochastic Calculus for Finance II

Shreve2004

Convex Optimization

Boyd & Vandenberghe2004

Reinforcement Learning

Sutton2018

The Principles of Diffusion Models

Lai & Song2024

All of Nonparametric Statistics

Wasserman2006

On Neural Differential Equations

Kidger2021