Asset Pricing Without Probability

Abstract

In this paper we propose a model of financial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite finite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, based on some new results on finitely additive measures. From this representation we derive a modified version of the Capital Asset Pricing Model according to which the expected value of augmented asset returns is explained by correlation with the market price of risk. In general this conclusion need not be true for original returns and this is shown to imply deviations from the CAPM that may potentially contribute to explain the equity premium puzzle. We also discuss the implications of the absence of free lunches.

Keywords: Arbitrage, Asset bubbles, Asset pricing, CAPM, Finitely additive measures, Finitely additive conditional expectation, Free lunch, Fundamental theorem of asset pricing, Martingale measure, Semimartingales

JEL Classification: G10, G12