Model-free Representation of Pricing Rules as Conditional Expectations

Sara Biagini and Rama Cont
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Sara Biagini: Università degli Studi di Perugia, Italy
Rama Cont: Centre de Mathématiques Appliquées, Ecole Polytechnique, France

Chapter 3 in Stochastic Processes and Applications to Mathematical Finance, 2007, pp 53-66 from World Scientific Publishing Co. Pte. Ltd.

Abstract: 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.

Keywords: Stochastic Calculus; Mathematical Finance; Insider Trading; Stochastic Control; Real Options; Filtering Model of Credit Risks; Stochastic Growth Models (search for similar items in EconPapers)
Date: 2007
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