Statistical inference for tail-based cumulative residual entropy

Sun, Hongfang; Chen, Yu; Hu, Taizhong

doi:10.1016/j.insmatheco.2022.01.002

Cited by 3 publications

(4 citation statements)

References 29 publications

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“…where h(t) = 1 − h(1 − t). The hypothesis of the dual theory in our context is that agents will choose among random variables to minimize (28). Given X and Y , we can write A nth dual risk averter prefers X to Y if this difference is positive, which happens whenever conditions (a) and (b) in Definition 1 hold.…”

Section: Discussionmentioning

confidence: 99%

Ordering Higher Risks in Yaari's Dual Theory

et al. 2023

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Section: Discussionmentioning

confidence: 99%

Ordering Higher Risks in Yaari's Dual Theory

et al. 2023

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“…., Y d . For related investigations from the statistical perspective, we refer the reader to El Methni et al [17], Cai et al [8], Acharya et al [1], Hou and Wang [22], and Sun et al [41].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Chen and Liu [11] extended the work of Tang and Yuan [42] to allow an asymptotic independence structure among , …, . For related investigations from the statistical perspective, we refer the reader to El Methni et al [17], Cai et al [8], Acharya et al [1], Hou and Wang [22], and Sun et al [41].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic results on tail moment and tail central moment for dependent risks

2023

Adv. Appl. Probab.

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In this paper, we consider a financial or insurance system with a finite number of individual risks described by real-valued random variables. We focus on two kinds of risk measures, referred to as the tail moment (TM) and the tail central moment (TCM), which are defined as the conditional moment and conditional central moment of some individual risk in the event of system crisis. The first-order TM and the second-order TCM coincide with the popular risk measures called the marginal expected shortfall and the tail variance, respectively. We derive asymptotic expressions for the TM and TCM with any positive integer orders, when the individual risks are pairwise asymptotically independent and have distributions from certain classes that contain both light-tailed and heavy-tailed distributions. The formulas obtained possess concise forms unrelated to dependence structures, and hence enable us to estimate the TM and TCM efficiently. To demonstrate the wide application of our results, we revisit some issues related to premium principles and optimal capital allocation from the asymptotic point of view. We also give a numerical study on the relative errors of the asymptotic results obtained, under some specific scenarios when there are two individual risks in the system. The corresponding asymptotic properties of the degenerate univariate versions of the TM and TCM are discussed separately in an appendix at the end of the paper.

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“…These shortfalls of entropy can be used to capture the variability of a financial position. For specific financial applications, we can refer to [5,7,8]. To this aim, we give covariance and Choquet integral representations for some entropies, and provide upper bounds of those entropies.…”

Section: Introductionmentioning

confidence: 99%

Covariance Representations and Coherent Measures for Some Entropies

Zuo,

Yin

2023

Entropy

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We obtain covariance and Choquet integral representations for some entropies and give upper bounds of those entropies. The coherent properties of those entropies are discussed. Furthermore, we propose tail-based cumulative residual Tsallis entropy of order α (TCRTE) and tail-based right-tail deviation (TRTD); then, we define a shortfall of cumulative residual Tsallis (CRTES) and shortfall of right-tail deviation entropy (RTDS) and provide some equivalent results. As illustrated examples, the CRTESs of elliptical, inverse Gaussian, gamma and beta distributions are simulated.

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Statistical inference for tail-based cumulative residual entropy

Cited by 3 publications

References 29 publications

Ordering Higher Risks in Yaari's Dual Theory

Ordering Higher Risks in Yaari's Dual Theory

Asymptotic results on tail moment and tail central moment for dependent risks

Covariance Representations and Coherent Measures for Some Entropies

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