The 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.

中文翻译：

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一般空间的失真风险度量

失真风险度量的类别是通过有符号的 Choquet 积分定义的，它包括金融和精算学文献中的许多经典风险度量、偏差度量和其他泛函。我们在一般模型空间上获得了表征、有限性、凸性和连续性结果，扩展了现有文献中关于失真风险度量和有符号 Choquet 积分的各种结果。本文提供了一个全面的失真风险度量理论结果工具包，可在应用中使用。