Some asymptotic results for sums of dependent random variables, with actuarial applications

Laeven, Roger J. A.; Goovaerts, Marc; Hoedemakers, Tom

doi:10.1016/j.insmatheco.2005.05.009

Cited by 21 publications

(11 citation statements)

References 13 publications

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“…For example, we see in Section 3 that relation (18) for the class is an immediate consequence of relation (17) for the class ERV. For the case of ERV, we have to present the desired asymptotic result as relation (17) instead of relation (18). This suggests that, when deriving tail asymptotics for the finite or infinite sum of randomly weighted subexponential random variables, we must pursue a relation similar to relation (17) rather than relation (18).…”

Section: Heavy-tailed Distributionsmentioning

confidence: 99%

“…Moreover, Tang and Tsitsiashvili [30] , Goovaerts et al [12] , and Wang and Tang [32] examined the asymptotic tail behavior of weighted sums in which the weights are positive random variables and can be arbitrarily dependent. Laeven et al [18] , Chen and Ng [4] , and Tang and Vernic [31] applied such results to insurance and finance. All these works confirm the principle of a single big jump for various dependent cases.…”

Section: Introductionmentioning

confidence: 97%

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Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation

2009

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Section: Heavy-tailed Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation

2009

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“…Heavy-tailed risks provide appropriate mathematical models for low-probability high-impact events, such as financial or environmental catastrophes; see e.g., Laeven, Goovaerts and Hoedemakers (2005) and the references therein.…”

Section: Setting and Notationmentioning

confidence: 99%

Expected Utility and Catastrophic Risk

et al. 2014

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Chris Muris Department of Economics Simon Fraser UniversityOctober 6, 2014 * We are very grateful to Graciela Chichilnisky, John Einmahl, Reyer Gerlagh, Christian Groth, Johan Eyckmans, Sjak Smulders, Peter Wakker, Aart de Zeeuw, Amos Zemel, and seminar and conference participants at Kyushu University, Tilburg University, the University of Copenhagen, EAERE, and the Tilburg Sustainability Center for helpful comments. This research was funded in part by the Japan Society for the Promotion of JEL Classification: D61; D81; G10; G20; Q5.

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“…The following three lemmas are due to [4,17,14] and are used in the development of Example 4 in Section 4.…”

Section: Definitions and Basic Propertiesmentioning

confidence: 99%

On Sums of Conditionally Independent Subexponential Random Variables

Foss

Richards

2010

Mathematics of OR

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The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random variables, for both deterministic and random sums, using a fresh approach, by considering conditional independence structures on the random variables. We seek sufficient conditions for the results of the theory with independent random variables still to hold. For a subexponential distribution, we introduce the concept of a boundary class of functions, which we hope will be a useful tool in studying many aspects of subexponential random variables. The examples we give in the paper demonstrate a variety of effects owing to the dependence, and are also interesting in their own right.

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Some asymptotic results for sums of dependent random variables, with actuarial applications

Cited by 21 publications

References 13 publications

Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation

Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation

Expected Utility and Catastrophic Risk

On Sums of Conditionally Independent Subexponential Random Variables

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