Asymptotic results on marginal expected shortfalls for dependent risks

Li, Jinzhu

doi:10.1016/j.insmatheco.2021.12.003

Cited by 4 publications

(8 citation statements)

References 40 publications

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“…Figures 3(i, ii) and 4(i, ii) indicate that a lighter tail of X 1 or a larger value of θ may lead to faster convergence rates for both R k (t), and we will not pursue it in this paper. The reader is referred to Section 5.1 of Li [34] for analytical asymptotic results on R (1) TM,1 (t) in some special cases of Scenario 4.1.…”

Section: Numerical Study On Relative Errorsmentioning

confidence: 99%

“…This task is essentially related to second-order asymptotic results on and , and we will not pursue it in this paper. The reader is referred to Section 5.1 of Li [34] for analytical asymptotic results on in some special cases of Scenario 4.1.…”

Section: Numerical Study On Relative Errorsmentioning

confidence: 99%

“…On the other hand, assuming that , …, are non-negative and have distributions from the Fréchet or Gumbel max-domain of attraction (MDA), Asimit et al [2] obtained a series of asymptotic formulas for as under certain dependence structures, including both the asymptotic independence and asymptotic dependence cases. Some of the results in Asimit et al [2] were extended to more general frameworks in the recent work of Li [34]. See Joe and Li [26], Hua and Joe [23], Zhu and Li [45], and Kley et al [29] for related discussions under the assumption that is of multivariate regular variation.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Numerical Study On Relative Errorsmentioning

confidence: 99%

Section: Numerical Study On Relative Errorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2023

Adv. Appl. Probab.

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“…For example the motor insurance and immobility insurance can be both relevant to a severe earthquake. For dependence among main claims we refer to [23], [8], [53], [25] and [9] for risk theory applications and to [41], [43] and [7] for risk management applications.…”

Section: Introductionmentioning

confidence: 99%

“…Follows directly from combination of parts 1. and 4.. Now we examine the closure property with respect to minimum in the same distribution class, but under another dependence structure. The minimum is not so popular, however in some application of risk management, as for example in marginal expected shortfall, see [41], it is helpful to know whether the marginal class remains after the minimum.…”

Section: Introductionmentioning

confidence: 99%

On the non-closure under convolution for strong subexponential distributions

Konstantinides

Leipus²,

Šiaulys³

2022

NAMC

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In this paper, we consider the convolution closure problem for the class of strong subexponential distributions, denoted as S*. First, we show that, if F, G ∈ L, then inclusions of F*G, FG, and pF + (1 – p)G for all (some) p ∈ (0; 1) into the class S* are equivalent. Then, using examples constructed by Klüppelberg and Villasenor [The full solution of the convolution closure problem for convolution-equivalent distributions, J. Math. Anal. Appl., 41:79–92, 1991], we show that S* is not closed under convolution.

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On the Tail Behavior for Randomly Weighted Sums of Dependent Random Variables with its Applications to Risk Measures

Chen,

Cheng

2024

Methodol Comput Appl Probab

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Asymptotic results on marginal expected shortfalls for dependent risks

Cited by 4 publications

References 40 publications

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

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

On the non-closure under convolution for strong subexponential distributions

On the Tail Behavior for Randomly Weighted Sums of Dependent Random Variables with its Applications to Risk Measures

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