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.
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.