April 12, 2007 The Fundamental Theorems of Prevision Summary: April 12, 2007 The Fundamental Theorems of Prevision and Asset Pricing Mark Schervish, Teddy Seidenfeld, Joseph B. Kadane We explore the connections between the concepts of coherence, as defined by deFinetti, and arbitrage in financial markets. 1. Introduction. Let be a set of states with a -field of subsets A. Let X stand for a set of measurable real-valued functions defined on . 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. DeFinetti took the concept of random variables as gambles very seriously, and used the concept to motivate the familiar concepts of probability and expectation. For each gamble X, he assumed that "You" would assign a value P(X), called the prevision of X so that you would be willing to accept the gamble [X - P(X)] as fair for all positive and negative values . The only constraint that deFinetti envisioned for you and your previsions is that you insisted that there be no positive amount that you had to lose for sure. For example, you would not be allowed to call a gamble fair if its supremum were negative. On the other hand, the criterion is weak enough to allow you call a gamble fair if its supremum is 0, even if all of Collections: Mathematics