Blog
The Kelly Criterion: Why Parallel Bets Increase Risk
An exploration of the Kelly criterion for optimal bet sizing, with mathematical derivations showing why it works for sequential bets but becomes dangerous with parallel positions.
Mordell's Theorem and Elliptic Curves
A journey through algebraic geometry, from Bezout's theorem to proving that the group of rational points on an elliptic curve is finitely generated.
The Orange-Jazztel Merger: A Competition Policy Case Study
An industrial economics analysis of the 2014 Orange-Jazztel merger in Spain, examining market power, competition concerns, and the European Commission's regulatory response.
Scenario Generation for Energy Market Modeling: Finding the Right Balance
Comparing scenario generation methods for stochastic optimization in European power markets under renewable energy uncertainty.
Robot Inverse Kinematics: A Non-Convex Optimization Challenge
Solving robot inverse kinematics and optimal trajectory planning using BFGS quasi-Newton methods, quadratic penalty methods, and logarithmic barrier functions.