MediMath Science

 In this blog, I provide a brief introduction to the famous Black–Scholes partial differential equation and examine it from Charlie Munger's critical perspective. While the equation revolutionized option pricing and became a cornerstone of modern quantitative finance, its assumptions may limit its usefulness when applied to long-term stock investing. Before proceeding, I should note that I am not an expert in this field. The Black–Scholes framework begins with the assumption that a stock price follows a stochastic process, $dS=\mu Sdt+\sigma S dW$, where $S$ denotes the stock price, $\mu$ is the expected growth rate, $\sigma$ represents volatility, and $dW$ is Brownian motion. In essence, stock prices are modeled as evolving continuously through a combination of deterministic growth and random uncertainty. Using stochastic calculus, one arrives at $\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2V}{\partial S^2}+rS\frac{\partial V}{\partial S}-rV=0,$ where $V$ i...

I have watched a few recent UFC fights, and the bout between Ilia Topuria and Justin Gaethje in mid-June 2026 was particularly memorable. Most people predicted a victory for Ilia, but the outcome was different from expectations. Both fighters displayed exceptional stamina and endurance, suggesting that they had invested a tremendous amount of time in training. However, some analysts believe that although Ilia preferred high-intensity training camps, he may have absorbed fewer realistic punches in sparring because his training partners were reluctant to engage him at full intensity due to the risk of being knocked out by his formidable punching power. Many critics dismiss mixed martial arts as little more than a modern version of Roman gladiatorial combat.  (The comparison, however, is imperfect. Gladiators were often forced into combat, whereas UFC fighters voluntarily dedicate years of their lives to earning a place among the sport's elite. Countless athletes train relentlessly fo...