A linear-quadratic HJB model that makes the stagflation trap mathematically precise: why a persistent supply shock forces the optimal steady state away from zero inflation and zero output gap simultaneously.
Epicurus added the clinamen — a random, uncaused swerve — to save atomism from determinism. Two thousand years later, it became the diffusion term in every SDE ever written.
McKean-Vlasov SDEs emerged from plasma physics in the 1960s. Mean field games arrived from economics in 2006. They converged on the same equation from opposite directions.
How Markov chains model checkout queues and customer flow — and what the stationary distribution tells a supermarket manager about staffing and store layout.
The Kelly criterion and Black-Scholes option pricing are the same mathematical object viewed from different angles. Both lead to the growth-optimal portfolio — Platen’s benchmark — which prices derivatives under the real-world measure without requiring a risk-neutra…
A 60/40 coin. A provably optimal betting strategy. And almost nobody uses it. Kelly’s 1956 result is one of the few places in finance where the correct answer is known and rationally ignored.
The bookmaker is not running a gambling operation. They are constructing a risk-neutral measure. Understanding that changes everything about how you think about betting strategies — including why Martingale fails even when you have edge.
Smoot-Hawley was not unique. From Versailles to Vietnam to Stalin’s grain quotas to the Maginot Line — the same pattern recurs. A model that forgets the other agents in the system.
In 1930, a thousand economists begged Hoover not to sign the Smoot-Hawley tariff. He signed it anyway. An agent-based model would have shown exactly what happened next — before it happened.
