TVaR-based capital allocation for multivariate compound distributions with positive continuous claim amounts

Cossette, Hélène; Mailhot, Mélina; Marceau, Étienne

doi:10.1016/j.insmatheco.2011.11.006

Cited by 42 publications

(34 citation statements)

References 18 publications

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“…The focus of the 2012 publications, however, is on applying such measures in the property–casualty insurance industry to: capital allocation (see Cossette et al. ), optimal reinsurance (see Lu et al. ), and risk transfer (see Guerra and Centeno, ).…”

Section: Resultsmentioning

confidence: 99%

Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update

Biener

Eling

2013

Risk Manage Insurance Review

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This article reports the main results of the 2012 Risk Premium Project update, a yearly review of actuarial and finance literature on the theory and empirics of risk assessment for property-casualty insurance. Pricing and modeling insurance risks and methodological advancement in risk valuation were popular fields of research in 2012. Of special note is new work on behavioral pricing and liquidity. Additionally, underwriting cycles attracted some controversy, and emerging risks, such as systemic risk and potential interrelations between insurance and other financial markets, were also areas of intense discussion.

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Section: Resultsmentioning

confidence: 99%

Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update

Biener

Eling

2013

Risk Manage Insurance Review

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“…Frees, Myers and Cummings [11] have introduced a multivariate frequency and severity model for home-owner insurance. Cossette, Mailhot and Marceau [5] have studied capital allocations with a multivariate compound risk model where claim frequencies are associated by copulas. Shi and Valdez [32] have explored the multivariate negative binomial distribution constructed through common shocks as well as through copulas and then applied it to model claim frequencies of three types of auto claims: third party property damage, own damage, and third party bodily injury.…”

Section: Introductionmentioning

confidence: 99%

CMPH: a multivariate phase-type aggregate loss distribution

Ren

Zitikis

2017

Dependence Modeling

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Abstract:We introduce a compound multivariate distribution designed for modeling insurance losses arising from di erent risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses. We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations of the aggregate loss to individual types of risk sources. Explicit formulas for the joint moment generating function and the joint moments of di erent loss types are derived, and recursive formulas for calculating the joint distributions given. Several special cases of particular interest are analyzed. An illustrative numerical example is provided.

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“…Previous studies have focused on particular probability distributions of losses (Cossette et al, 2012(Cossette et al, , 2013, on alternative dependence structures between risks (Cai and Wei, 2014), on asymptotic allocations based on commonly used risk measures (Asimit et al, 2011) or on optimization function alterations in order to overcome limitations of the loss function minimization allocation criterion (Xu and Hu, 2012;Xu and Mao, 2013). An exhaustive list is not provided here but it is the object of ongoing research.…”

Section: Introductionmentioning

confidence: 99%

Compositional methods applied to capital allocation problems

Belles-Sampera¹,

Guillén²,

Santolino³

2016

JOR

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In this article we examine the relationship between capital allocation problems and compositional data, i.e., information that refers to the parts of a whole conveying relative information. We show that capital allocation principles can be interpreted as compositions. The natural geometry and vector space structure of compositional data are used to operate with capital allocation solutions. The distance and average that are appropriated in the geometric structure of compositions are presented. We demonstrate that these two concepts can be used to compare capital allocation principles and to merge them. An illustration is provided to show how the distance between capital allocation solutions and the average of these solutions can be computed, and interpreted, by risk managers in practice.JEL classification: C02, G22, D81.

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TVaR-based capital allocation for multivariate compound distributions with positive continuous claim amounts

Cited by 42 publications

References 18 publications

Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update

Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update

CMPH: a multivariate phase-type aggregate loss distribution

Compositional methods applied to capital allocation problems

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