The Fundamental Theorems of Prevision and Asset Pricing

We explore the connections between the concepts of coherence, as defined by deFinetti, and arbitrage in financial markets. 1. Introduction. Let Ω be a set of states with a σ-field of subsets A. Let X stand for a set of measurable real-valued functions defined on Ω. Whether X contains unbounded functions will be made clear in each context. The elements of X will be called gambles, risky assets, or random variables. Functions of elements of X will also be called by those same names