 Fundamental theorem of asset pricing

In a finite market, absence of arbitrage is equivalent to the existence of an equivalent martingale measure. If that measure is unique, every contingent claim has a unique no-arbitrage price given by its discounted expectation.

The Fundamental Theorem of Asset Pricing is a key concept in financial mathematics and economics that establishes a connection between the pricing of financial assets and the existence of arbitrage opportunities in a market. It essentially provides the theoretical foundation for understanding how assets should be priced in a no-arbitrage market. The theorem can be summarized in a few main points: 1. **No Arbitrage Condition**: The first part of the theorem states that if there are no arbitrage opportunities in a market (i.e.