Skip to main content

Set-valued shortfall and divergence risk measures

Author(s): Ararat, Çağın; Hamel, Andreas H.; Rudloff, Birgit

To refer to this page use:
Abstract: Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate risk measures is constructed via a recent Lagrange duality for set optimization. In particular, it is shown that a shortfall risk measure can be written as an intersection over a family of divergence risk measures indexed by a scalarization parameter. Examples include set-valued versions of the entropic risk measure and the average value at risk. As a second step, the minimization of these risk measures subject to trading opportunities is studied in a general convex market in discrete time. The optimal value of the minimization problem, called the market risk measure, is also a set-valued risk measure. A dual representation for the market risk measure that decomposes the effects of the original risk measure and the frictions of the market is proved.
Publication Date: Sep-2017
Citation: Ararat, Çağın, Hamel, Andreas H., Rudloff, Birgit. (2017). Set-valued shortfall and divergence risk measures. International Journal of Theoretical and Applied Finance 20 (5) 1750026, doi:10.1142/S0219024917500261
DOI: doi:10.1142/S0219024917500261
Pages: 1 - 42
Type of Material: Journal Article
Journal/Proceeding Title: International Journal of Theoretical and Applied Finance
Version: Author's manuscript

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.