Nonparametric inference for sensitivity of Haezendonck–Goovaerts risk measure

Wang, Xing; Liu, Qing; Hou, Yanxi; Peng, Liang

doi:10.1080/03461238.2018.1429299

Cited by 8 publications

(2 citation statements)

References 30 publications

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“…Derivatives of distortion risk measures, applied to a model output in the direction of an input, have been extensively studied in sensitivity analysis and in capital allocation; notably by Hong (2009); Cont et al (2010) for the VaR risk measure, Hong and Liu (2009) for the ES risk measure and Tsanakas and Millossovich (2016) for general distortion risk measures. Sensitivity to linear portfolios summarized by Haezendonck-Goovaerts and entropic risk measures are considered in Wang et al (2018) and Tsanakas (2009), respectively. Cao and Wan (2017) analyse derivatives of expected utilities in connection to optimal portfolio selection, while Gourieroux et al (2000Gourieroux et al ( , 2006 consider directional derivatives of distortion risk measures with respect to parameter uncertainty for linear aggregation functions.…”

Section: Relation To Existing Literaturementioning

confidence: 99%

Cascade Sensitivity Measures

2018

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In risk analysis, sensitivity measures quantify the extent to which the probability distribution of a model output is affected by changes (stresses) in individual random input factors. For input factors that are statistically dependent, we argue that a stress on one input should also precipitate stresses in other input factors. We introduce a novel sensitivity measure, termed cascade sensitivity, defined as a derivative of a risk measure applied on the output, in the direction of an input factor. The derivative is taken after suitably transforming the random vector of inputs, thus enabling the cascade sensitivity measure to capture both the direct impact of the stressed input factor on the output, as well as indirect effects via other input factors that are dependent on the one being stressed. Alternative representations of the cascade sensitivity measure, which can be calculated from a single Monte Carlo sample, are provided for two types of stress: a) a perturbation of the distribution of an input factor such that the stressed input follows a mixture distribution, and b) an additive random shock applied to the input factor. The calculation of those representations does not require simulating under different model specifications or the explicit study of the properties of the model function, making the proposed method attractive for applications, as illustrated through numerical examples.

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Section: Relation To Existing Literaturementioning

confidence: 99%

Cascade Sensitivity Measures

2018

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“…The original formulation was extended by Goovaerts et al [13] and by Bellini and Rosazza Gianin [4] to account for general (not necessarily positive) losses. The extended formulation is known under the name of Haezendonck-Goovaerts premium principle (or equivalently Haezendonck-Goovaerts risk measure) and has been the subject of extensive study in the literature, see Bellini and Rosazza Gianin [5] and [6], Goovaerts et al [15], Mao and Hu [18], Tang and Yang [21] and [22], Zhu et al [26], Ahn and Shyamalkumar [1], Peng et al [20], Wang and Peng [24], Liu et al [17], Wang et al [23]. Moreover, we refer to the general survey by Goovaerts and Laeven [14].…”

Section: Introductionmentioning

confidence: 99%

Stability properties of Haezendonck-Goovaerts premium principles

Gao

Munari

Xanthos

2019

Preprint

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We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always satisfy the Fatou property. This allows to establish a tractable dual representation without imposing any condition on the reference Orlicz function. In addition, we show that Haezendonck-Goovaerts principles satisfy the stronger Lebesgue property if and only if the reference Orlicz function fulfills the so-called ∆ 2 condition.

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