DISTORTION RISKMETRICS ON GENERAL SPACES

2020 ◽  
Vol 50 (3) ◽  
pp. 827-851 ◽  
Author(s):  
Qiuqi Wang ◽  
Ruodu Wang ◽  
Yunran Wei
Keyword(s):  
General Model ◽  
Risk Measures ◽  
Actuarial Science ◽  
Model Spaces ◽  
Choquet Integrals ◽  
Theoretical Results ◽  
Distortion Risk Measures

AbstractThe class of distortion riskmetrics is defined through signed Choquet integrals, and it includes many classic risk measures, deviation measures, and other functionals in the literature of finance and actuarial science. We obtain characterization, finiteness, convexity, and continuity results on general model spaces, extending various results in the existing literature on distortion risk measures and signed Choquet integrals. This paper offers a comprehensive toolkit of theoretical results on distortion riskmetrics which are ready for use in applications.

Equivalent Distortion Risk Measures on Moment Spaces

2018 ◽  
Author(s):  
Dries Cornilly ◽  
Steven Vanduffel
Keyword(s):  
Risk Measures ◽  
Moment Spaces ◽  
Distortion Risk Measures

Estimation of Distortion Risk Measures

2013 ◽  
Vol 12 (1) ◽  
pp. 213-235 ◽  
Author(s):  
H. Tsukahara
Keyword(s):  
Risk Measures ◽  
Distortion Risk Measures

scholarly journals Distortion Risk Measures in Portfolio Optimization

2010 ◽  
pp. 649-673 ◽  
Author(s):  
Ekaterina N. Sereda ◽  
Efim M. Bronshtein ◽  
Svetozar T. Rachev ◽  
Frank J. Fabozzi ◽  
Wei Sun ◽  
...  
Keyword(s):  
Portfolio Optimization ◽  
Risk Measures ◽  
Distortion Risk Measures

Limit Theory for Forecasts of Extreme Distortion Risk Measures and Expectiles*

2019 ◽  
Author(s):  
Yannick Hoga
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Limit Theory ◽  
Extreme Risk ◽  
Wide Range ◽  
Scale Models ◽  
Adequate Coverage ◽  
Nonparametric Alternatives ◽  
Do So ◽  
Distortion Risk Measures

Abstract We develop central limit theory for tail risk forecasts in general location–scale models. We do so for a wide range of risk measures, viz. distortion risk measures (DRMs) and expectiles. Two popular members of the class of DRMs are the Value-at-Risk and the Expected Shortfall. The forecasts we consider are motivated by a Pareto-type tail assumption for the innovations and allow for extrapolation beyond the range of available observations. Simulations reveal adequate coverage of the forecast intervals derived from the limit theory. An empirical application demonstrates that our estimators outperform nonparametric alternatives when forecasting extreme risk in sufficiently large samples.

SET-VALUED LAW INVARIANT COHERENT AND CONVEX RISK MEASURES

2019 ◽  
Vol 22 (03) ◽  
pp. 1950004 ◽  
Author(s):  
YANHONG CHEN ◽  
YIJUN HU
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Convex Risk Measures ◽  
New Class ◽  
The Relationship ◽  
Distortion Risk Measures

In this paper, we investigate representation results for set-valued law invariant coherent and convex risk measures, which can be considered as a set-valued extension of the multivariate scalar law invariant coherent and convex risk measures studied in the literature. We further introduce a new class of set-valued risk measures, named set-valued distortion risk measures, which can be considered as a set-valued version of multivariate scalar distortion risk measures introduced in the literature. The relationship between set-valued distortion risk measures and set-valued weighted value at risk is also given.

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