This work has been supported by the Hungarian National Foundation for Scientific Research under Grant K105840 and by the Austrian Forschungsförderungsgesellschaft in its Josef Ressel Centre for Optimisation under Uncertainty. The second author has benefited from discussions with František Matúš.
MEASURING DISTRIBUTION MODEL RISK
Article first published online: 9 OCT 2013
© 2013 Wiley Periodicals, Inc.
How to Cite
Breuer, T. and Csiszár, I. (2013), MEASURING DISTRIBUTION MODEL RISK. Mathematical Finance. doi: 10.1111/mafi.12050
- Article first published online: 9 OCT 2013
- Manuscript Accepted: MAY 2013
- Manuscript Received: FEB 2012
- Hungarian National Foundation for Scientific Research. Grant Number: K105840
- Austrian Forschungsförderungsgesellschaft in its Josef Ressel Centre for Optimisation under Uncertainty
- multiple priors;
- divergence preferences;
- relative entropy;
- Bregman distance;
- maximum entropy principle;
- convex integral functional;
- generalized exponential family
We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy or another f-divergence or Bregman distance. We use the theory of minimizing convex integral functionals under moment constraints to give formulae for the calculation of distribution model risk and to explicitly determine the worst case distribution from the set of plausible distributions. We also evaluate related risk measures describing divergence preferences.