# The Fundamental Theorem of Asset Pricing is Bayesianism

2017-Aug-17If uncertainties encode bet preferences as represented by probabilities, Bayesianism is a collection of Dutch book arguments proving that probabilities must be consistent with each other (defining a probability measure) to be rational. Weisberg has an excellent paper that explains the details. On the other hand, the Fundamental Theorem of Asset Pricing proves that for prices to be arbitrage-free, they must be conditional expectations. Details on the relevant results are found in “The Mathematics of Arbitrage”, by Delbaen and Schachermayer. Having a consistent probability function has been shown to be equivalent to minimizing a proper scoring rule. And conditional expectations have been shown to minimize Bregman divergences. Et cetera. The correspondance between these theories is alluded to by Nau.