Distortion risk measures, ROC curves, and distortion divergence-Reference-Cited by-同舟云学术

Distortion risk measures, ROC curves, and distortion divergence

Published:2017-11-11 Issue:1-2 Volume:35 Page:35-50
ISSN:2196-7040
Container-title:Statistics & Risk Modeling
language:en
Short-container-title:

Author:

Schumacher Johannes M.¹^ORCID

Affiliation:

1. Faculty of Economics and Business , Section Quantitative Economics , University of Amsterdam , Roetersstraat 11 , Amsterdam , Netherlands

Abstract

Abstract Distortion functions are employed to define measures of risk. Receiver operating characteristic (ROC) curves are used to describe the performance of parametrized test families in testing a simple null hypothesis against a simple alternative. This paper provides a connection between distortion functions on the one hand, and ROC curves on the other. This leads to a new interpretation of some well-known classes of distortion risk measures, and to a new notion of divergence between probability measures.

Publisher

Walter de Gruyter GmbH

Subject

Statistics, Probability and Uncertainty,Modeling and Simulation,Statistics and Probability

Link

https://www.degruyter.com/document/doi/10.1515/strm-2017-0012/pdf

Reference40 articles.

1. D. Aldous and P. Diaconis, Strong uniform times and finite random walks, Adv. in Appl. Math. 8 (1987), 69–97. 10.1016/0196-8858(87)90006-6

2. B. C. Arnold, C. A. Robertson, P. L. Brockett and B.-Y. Shu, Generating ordered families of Lorenz curves by strongly unimodal distributions, J. Bus. Econom. Statist. 5 (1987), 305–308.

3. P. Artzner, F. Delbaen, J.-M. Eber and D. Heath, Coherent measures of risk, Math. Finance 9 (1999), 203–228. 10.1111/1467-9965.00068

4. H. Assa, On optimal reinsurance policy with distortion risk measures and premiums, Insurance Math. Econom. 61 (2015), 70–75. 10.1016/j.insmatheco.2014.11.007

5. A. G. Balter and A. Pelsser, Quantifying ambiguity bounds through hypothetical statistical testing, Working paper (2017), 10.2139/ssrn.2613843.