Model-free representation of pricing rules as conditional expectations

We introduce a distinction between model-based and model-free arbitrage and formulate an operational de nition for absence of model-free arbitrage in a nancial market, in terms of a set of minimal requirements for the pricing rule prevailing in the market. We show that any pricing rule verifying these properties can be represented as a conditional expectation operator with respect to a probability measure under which prices of traded assets follow martingales. Our result can be viewed as a model-free version of the fundamental theorem of asset pricing, which does not require any notion of reference" probability measure.