Mathematics and Financial Economics

, Volume 12, Issue 2, pp 219–247 | Cite as

Disentangling price, risk and model risk: V&R measures



We propose a method to assess the intrinsic risk carried by a financial position X when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex duality in a Knightian setting, where a family of probability measures replaces the single reference probability and is then applied to value financial positions. Diametrically, our construction of Value and Risk measures is based on the selection of a basket of claims to test the reliability of models. We compare a random payoff X with a given class of derivatives written on X, and use these derivatives to “test” the pricing measures. We further introduce and study a general class of Value and Risk measures \( R(p,X,\mathbb {P})\) that describes the additional capital that is required to make X acceptable under a probability \(\mathbb {P}\) and given the initial price p paid to acquire X.


Model risk Pricing uncertainty Test functions Value and Risk measures Law invariant risk measures Quasi-convex duality 

JEL Classification

C02 G10 G12 G32 D46 D81 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Università degli Studi di MilanoMilanItaly

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