Page "Fundamental theorem of asset pricing" Paragraph 0

The fundamental theorems of arbitrage / finance provide necessary and sufficient conditions for a market to be arbitrage free and for a market to be complete.

An arbitrage opportunity is a way of making money with no initial investment without any possibility of loss.

Though arbitrage opportunities do exist briefly in real life, it has been said that any sensible market model must avoid this type of profit.

The first theorem is important in that it ensures a fundamental property of market models.

Completeness is a common property of market models ( for instance the Black – Scholes model ).

A complete market is one in which every European option can be replicated.

Though this property is common in models, it is not always considered desirable or realistic.