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Open AccessFeature PaperArticle

Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion

1
msg life Austria Ges.m.b.H., Ausstellungsstraße 50, 1020 Vienna, Austria
2
Department of Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstraße 8–10/E105-1, 1040 Vienna, Austria
*
Author to whom correspondence should be addressed.
Risks 2020, 8(2), 43; https://doi.org/10.3390/risks8020043
Received: 21 March 2020 / Revised: 25 April 2020 / Accepted: 27 April 2020 / Published: 2 May 2020
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics)
In this paper, we discuss a generalization of the collective risk model and of Panjer’s recursion. The model we consider consists of several business lines with dependent claim numbers. The distributions of the claim numbers are assumed to be Poisson mixture distributions. We let the claim causes have certain dependence structures and prove that Panjer’s recursion is also applicable by finding an appropriate equivalent representation of the claim numbers. These dependence structures are of a stochastic non-negative linear nature and may also produce negative correlations between the claim causes. The consideration of risk groups also includes dependence between claim sizes. Compounding the claim causes by common distributions also keeps Panjer’s recursion applicable. View Full-Text
Keywords: extended CreditRisk+; Poisson mixture distribution; dependence modelling; compound distribution; Panjer recursion extended CreditRisk+; Poisson mixture distribution; dependence modelling; compound distribution; Panjer recursion
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Rudolph, C.; Schmock, U. Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion. Risks 2020, 8, 43.

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