Systemic Risk: An Asymptotic Evaluation

Asimit, Alexandru V.; Li, Jinzhu

doi:10.1017/asb.2017.38

Cited by 17 publications

(5 citation statements)

References 25 publications

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“…The conditions regarding the marginal distributions of in Assumptions 3.1 and 3.2 guarantee the existence of the TM and TCM. The dependence structure defined by (3.1) and (3.2) was first proposed in Mitra and Resnick [37] and has been extensively studied and applied in risk theory; see Asimit et al [2], Hashorva and Li [21], and Asimit and Li [3]. Since , the relation (3.1) obviously implies pairwise asymptotic independence among , …, .…”

Section: Resultsmentioning

confidence: 99%

“…Some regulatory environments (e.g., the Swiss Solvency Test) require that the total capital of the system equals the conditional tail expectation of with respect to some threshold t , i.e., . Then the most intuitive and commonly used capital allocation rule is the famous Euler one, which assigns the amount of to the k th individual component; see Denault [13], Asimit and Li [3], and Baione et al [4]. There have been many fruitful contributions to the study of .…”

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: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2023

Adv. Appl. Probab.

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“…If the primary losses X 1 and X 2 have regularly varying distributions, the insurance system may collapse immediately. To prevent this potential scenario, scholars have proposed various risk measures or their variants, see Asimit and Li (2018a, b) [3,4], Acharya et al (2017) [1], Ji et al (2021) [23], Li (2022) [26], among many others, aiming at enhancing resilience to systemic shocks and promoting greater stability in the markets.…”

Section: Applications To Risk Measuresmentioning

confidence: 99%

“…No matter how, the primary objective is to assess the financial distress of a system caused by the collapse of a specific component within the financial system under consideration. In this paper, we study the SR formulated by Asimit and Li (2018a) [3] or Liu and Yang (2021) [28].…”

Section: An Application To Systemic Riskmentioning

confidence: 99%

On the tail behavior for randomly weighted sums of dependent random variables with its applications to risk measures

Chen,

Cheng

2024

Preprint

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This paper considers the asymptotic behavior for the tail probability of randomly weighted sum Sθ 2 = θ1X1+θ2X2, where X1, X2, θ1, and θ2 are non-negative dependent random variables with distributions F1, F2, G1, and G2, respectively. We obtain the tail-equivalence of P Sθ 2 > x and P(θ1X1 > x)+P(θ2X2 > x) as x → ∞ and some closure properties of distribution classes in three cases: (i). θ1, θ2 are bounded and F1, F2 are subexponential; (ii). θ1, θ2 satisfy the condition of Theorem 2.1 of Tang (2006) [33] and F1, F2 are subexponential with positive lower Matuszewska indices; (iii). θ1, θ2 satisfy the condition of Theorem 3.3 (iii) of Cline and Samorodnitsky (1994) [12] and F1, F2 are long-tailed and dominatedlyvarying- tailed. Furthermore, when F1 and F2 are regularly-varying-tailed, a more transparent result is established and applied to obtain asymptotic results for risk measures. Some numerical studies are conducted to check the accuracy of the obtained results.

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“…Calculating or estimating systemic risk allocations given an unconditional joint loss distribution is in general challenging since analytical calculations often require to know the joint distribution of the marginal loss and the aggregated loss, and crude Monte Carlo estimation suffers from the rare-event characters of the crisis event. For computing CoVaR, CoES and MES, Mainik and Schaanning (2014), Bernardi et al (2017) and Jaworski (2017) derived formulas based on the copula of the marginal and the aggregated loss; Asimit and Li (2018) derived asymptotic formulas based on extreme value theory; and Girardi and Ergün (2013) estimate CoVaR under a multivariate GARCH model. Chiragiev and Landsman (2007), Dhaene et al (2008), Furman and Landsman (2008) and Vernic (2006) calculated Euler allocations for specific joint distributions.…”

Section: Introductionmentioning

confidence: 99%

Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations

Koike

Hofert

2020

Risks

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We propose a novel framework of estimating systemic risk measures and risk allocations based on a Markov chain Monte Carlo (MCMC) method. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo methods often provide inefficient estimates due to the rare-event character of crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. Efficiency of the MCMC estimators are demonstrated in a series of numerical experiments.

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Systemic Risk: An Asymptotic Evaluation

Cited by 17 publications

References 25 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 tail behavior for randomly weighted sums of dependent random variables with its applications to risk measures

Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations

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