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Model spaces for risk measures

Institution:	1. Amsterdam School of Economics, University of Amsterdam, The Netherlands;2. Faculty of Actuarial Science and Insurance, Cass Business School, City University London, United Kingdom;3. RiskLab, Department of Mathematics, ETH Zurich, Switzerland;1. Department of Finance and Insurance, Hongik University, 2639 Sejong-ro, Jochiwon-eup, Sejong, 339-701, Republic of Korea;2. Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada;1. Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Abstract:	We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk measure respecting the underlying ambiguity profile. We particularly emphasise liquidity effects and discuss the correspondence between properties of the risk measure and the structure of this domain as well as subdifferentiability properties.

Keywords:	Model free risk assessment Extension of risk measures Continuity properties of risk measures Subgradients Implied reference models
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