Model-Free Representation of Pricing Rules as Conditional Expectations

AbstractWe formulate an operational definition for absence of model-free arbitrage in a financial market, in terms of a set of minimal requirements for the pricing rule prevailing in the market and without making reference to any ‘objective’ probability measure. 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 does not require any notion of “reference” probability measure and is consistent with the formulation of model calibration problems in option pricing.

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