Small dependencies and large actuarial risks

Willem Albers; Wilbert C.M. Kallenberg; Viktor Lukocius

Small dependencies and large actuarial risks

Willem Albers, Wilbert C.M. Kallenberg, Viktor Lukocius

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Abstract

Methods for computing risk measures such as stop-loss premiums tacitly assume independence of the underlying individual risks. From earlier studies it is already known that this assumption can lead to huge errors even when only small dependencies occur. In the present paper a general model is developed, which covers what happens in practice in a realistic way. Moreover, it is also flexible, in the sense that it allows application in practice. Approximations are presented which are both accurate and transparent and the results obtained are illustrated through some explicit examples.

Original language	Undefined
Place of Publication	Enschede
Publisher	University of Twente, Department of Applied Mathematics
Number of pages	19
Publication status	Published - Nov 2006

Publication series

Name	Memorandum
Publisher	University of Twente, Department of Applied Mathematics
No.	1812
ISSN (Print)	0169-2690

Keywords

MSC-62E17
MSC-62P05
Overdispersion
Tail events
Cumulants
Dependence
Aggregate claims

Access to Document

Albers2006smallFinal published version, 794 KB

Cite this

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AU - Lukocius, Viktor

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AB - Methods for computing risk measures such as stop-loss premiums tacitly assume independence of the underlying individual risks. From earlier studies it is already known that this assumption can lead to huge errors even when only small dependencies occur. In the present paper a general model is developed, which covers what happens in practice in a realistic way. Moreover, it is also flexible, in the sense that it allows application in practice. Approximations are presented which are both accurate and transparent and the results obtained are illustrated through some explicit examples.

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KW - Cumulants

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KW - Aggregate claims

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