The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 22, Number 1 (2012), 213-238.
Risk measuring under model uncertainty
The framework of this paper is that of risk measuring under uncertainty which is when no reference probability measure is given. To every regular convex risk measure on , we associate a unique equivalence class of probability measures on Borel sets, characterizing the riskless nonpositive elements of . We prove that the convex risk measure has a dual representation with a countable set of probability measures absolutely continuous with respect to a certain probability measure in this class. To get these results we study the topological properties of the dual of the Banach space L1(c) associated to a capacity c.
As application, we obtain that every G-expectation has a representation with a countable set of probability measures absolutely continuous with respect to a probability measure P such that P(|f|) = 0 if and only iff . We also apply our results to the case of uncertain volatility.
Ann. Appl. Probab. Volume 22, Number 1 (2012), 213-238.
First available in Project Euclid: 7 February 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46A20: Duality theory 91B30: Risk theory, insurance
Secondary: 46E05: Lattices of continuous, differentiable or analytic functions
Bion-Nadal, Jocelyne; Kervarec, Magali. Risk measuring under model uncertainty. Ann. Appl. Probab. 22 (2012), no. 1, 213--238. doi:10.1214/11-AAP766. https://projecteuclid.org/euclid.aoap/1328623699