ASSET PRICING WITHOUT PROBABILITY

Abstract. In this paper we propose a model of \u85nancial 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 \u85nite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, based on some new results on nitely additive measures. From this representation we derive a modi\u85ed 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. 1. Introduction. Continuous time \u85nancial models adopt a wide de\u85nition of the trading activity of agents, no matter the degree of market imperfections considered. The ground for such de\u85nition is laid by two basic assumptions (henceforth jointly referred to as the traditional setting): that a probability measure is given and that, with reference to this, gains from trade may be modeled as semimartingales. This framework has fostere