🤫 The Master Class · Part II — Mathematics I — Brownian Motion → the Closed Form

The mathematics of aloha, derived from the ground up. Geometric Brownian motion. Itô's lemma — falling out of a Taylor expansion, with the one fact that (dW)² = dt. The delta-hedged portfolio whose randomness cancels exactly. No-arbitrage, and the Black–Scholes PDE — where the drift μ simply vanishes, so we never need a view on direction. Then Girsanov and risk-neutral valuation, one Gaussian integral, and the closed form: C = S·Φ(d₁) − K·e^−rτ·Φ(d₂) — which is exactly bs_price in the engine. Seven steps, no magic, every boundary checked. This one formula is the ruler for the entire overlay.

The seven-part arc

~105 minutes, all the way down — building it, running it, and using it to manage permanent capital.

The Thesis & The Two North Stars ▶ Watch

Permanent capital, Simons × Munger, weight as cash, never overpay.

Mathematics I — Brownian Motion → the Closed Form ▶ Now playing

We derive Black–Scholes from the SDE; the drift μ simply disappears.

III

Mathematics II — The Greeks, the ★ Identity, Implied Vol ▶ Watch

Δ = Φ(d₁) proved; vega's wings; bisection over Newton.

Signals & The Overlay ▶ Watch

RSI as a 27-week EMA, sell-the-wall, the synthetic long, the ladder LP.

The Engine & The Citadel ▶ Watch

Constitution-as-code, Iron Rules, the 22% reserve, the ratchet.

The Scientific Method at Scale ▶ Watch

The wind tunnel, the independent auditor, publishing our mistakes.

VII

Running Client Capital ▶ Watch

Wire to invested, the cockpit, risk tiers, the IRR objective, the oath.

The Aloha Machine · The Master Class — training & educational content, open to everyone. Fund A is pre-launch; every figure shown is hypothetical and model-derived (SEC Rule 206(4)-1) and does not predict results. No roster or weights are shown. Not an offer to sell or a solicitation of an offer to buy any security. Leo is a fictional AI presenter; the voice is AI-generated — not a recording of any real person. 🤫 AlphaAlohaOS · Alphabets 27 · hushh