Mathematical Finance

The single principle underneath all of derivative pricing, made concrete in a one-period market.

Why the hedge cost equals a discounted expectation, and why the pricing measure makes discounted prices martingales.

No arbitrage \(\Leftrightarrow\) an equivalent martingale measure exists; completeness \(\Leftrightarrow\) it is unique.

Delta-hedging a continuously-traded option leads to a PDE whose solution is the closed-form price.

Mean–variance efficiency, expected-utility choice, and a first look at the Merton problem.