A general approach to full-range tail dependence copulas

Su, Jianxi; Hua, Lei

doi:10.1016/j.insmatheco.2017.08.009

Cited by 15 publications

(15 citation statements)

References 28 publications

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“…F Λ ∈ RV −γ that varies regularly at infinity with order −γ (Bingham et al 1987). The expressions for λ U and χ U are readily obtained by evoking Corollary 3.3 in Su and Hua (2017). This completes the proof of this proposition.…”

Section: Proof Of Propositionsupporting

confidence: 63%

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Semenikhine

Furman

2018

Risks

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Abstract:One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the same task is via an application of the Bernstein-Widder theorem with respect to a shifted inverse Beta probability density function. This way, which leads to an arguably equally popular multiplicative background risk model (MBRM), has been by far less investigated. In this paper, we reintroduce the multiplicative multivariate gamma (MMG) distribution in the most general form, and we explore its various properties thoroughly. Specifically, we study the links to the MBRM, employ the machinery of divided differences to derive the distribution of the aggregate risk random variable explicitly, look into the corresponding copula function and the measures of nonlinear correlation associated with it, and, last but not least, determine the measures of maximal tail dependence. Our main message is that the MMG distribution is (1) very intuitive and easy to communicate, (2) remarkably tractable, and (3) possesses rich dependence and tail dependence characteristics. Hence, the MMG distribution should be given serious considerations when modelling dependent risks.

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Section: Proof Of Propositionsupporting

confidence: 63%

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Semenikhine

Furman

2018

Risks

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“…Moreover, in order to obtain a better assessment of these copula-based models, one can complement the analysis made with the tail dependence, the Crámer-von Mises distance or the WRMSE, with a response-based analysis, as mentioned in [59] . Several models can be employed to model the met-ocean data and then used e.g.…”

Section: Discussion and Applications To Wind Engineeringmentioning

confidence: 99%

“…Therefore, other tail and asymptotic dependence analysis (e.g. Genest and Favre, 2007; Su and Lei, 2017) should be further implemented to improve the present research.…”

Section: Discussion and Applications To Wind Engineeringmentioning

confidence: 99%

“…Moreover, in order to obtain a better assessment of these copula-based models, one can complement the analysis made with the tail dependence, the Crámer–von Mises distance or the WRMSE, with a response-based analysis, as mentioned in Su and Lei (2017). Several models can be employed to model the met-ocean data and then used, for example, for loads estimations at an offshore wind turbine or for dragging forces acting on the soil–structure interaction, and then the behaviour of the response, say the loads in the first case, is further analysed.…”

Section: Discussion and Applications To Wind Engineeringmentioning

confidence: 99%

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Asymmetric copula–based distribution models for met-ocean data in offshore wind engineering applications

et al. 2018

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Joint statistical models for long-term wave climate are a key aspect of offshore wind engineering design. However, to find a joint model for sea-state characteristics is often difficult due to the complex nature of the wave climate and the physical constraints of seastate phenomena. The available records of wave heights and periods are often very asymmetric in their nature. This paper presents a copula-based approach to obtain the joint cumulative distribution function of significant wave heights and the mean up-crossing periods. This study is based on 124 months hindcast data concerning Horns Rev 3 offshore wind farm. The extra-parametrization technique of symmetric copulas is implemented to account for the asymmetry present in the data. The analysis of the total sea, the wind-sea and primary swell components is performed separately. The results show that the extraparametrization technique with pairwise copulas consistently provided a better goodnessof-fit when compared to symmetric copulas. Moreover, it is demonstrated that the separation of the total sea into its components does not always improve the extraparametrized copula's performance. Furthermore, this paper also discusses copula application to offshore wind engineering.

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“…3 Further analysis on copulas properties for tail dependency can be founs in Hua (2017), Su and Furman (2017), and Su and Hua (2017) 4 We consider risk-neutral implied interest rate swaption volatilities, as there exists no market price for counterparty credit risk and, as Stulz (2004) and Bolton and Oehmkez (2013) report, during times of distress financial institutions have misvalued OTC derivatives in favour of diminishing the collateral associated with the instruments held, which could mislead the study.…”

Section: Introductionmentioning

confidence: 99%

The Implications of Tail Dependency Measures for Counterparty Credit Risk Pricing

et al. 2020

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A general approach to full-range tail dependence copulas

Cited by 15 publications

References 28 publications

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Asymmetric copula–based distribution models for met-ocean data in offshore wind engineering applications

The Implications of Tail Dependency Measures for Counterparty Credit Risk Pricing

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