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

Cordelia Rudolph and Uwe Schmock
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Cordelia Rudolph: msg life Austria Ges.m.b.H., Ausstellungsstraße 50, 1020 Vienna, Austria
Uwe Schmock: Department of Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstraße 8–10/E105-1, 1040 Vienna, Austria

Risks, 2020, vol. 8, issue 2, 1-31

Abstract: 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.

Keywords: extended CreditRisk+; Poisson mixture distribution; dependence modelling; compound distribution; Panjer recursion (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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