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DOI: 10.5445/IR/1000013433
DOI: 10.1239/aap/1214950217
Zitationen: 2
Web of Science
Zitationen: 2

Multivariate risk processes with interacting intensities

Bäuerle, Nicole; Grübel, Rudolf

The classical models in risk theory consider a single type of claim. In the insurance business, however, several business lines with separate claim arrival processes appear naturally, and the individual claim processes may not be independent. We introduce a new class of models for such situations, where the underlying counting process is a multivariate continuous-time Markov chain of pure-birth type and the dependency of the components arises from the fact that the birth rate for a specific claim type may depend on the number of claims in the other component processes. Under certain conditions, we obtain a fluid limit, i.e. a functional law of large numbers for these processes. We also investigate the consequences of such results for questions of interest in insurance applications. Several specific subclasses of the general model are discussed in detail and the Cramér asymptotics of the ruin probabilities are derived in particular cases.

Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2008
Sprache Englisch
Identifikator ISSN: 0001-8678
URN: urn:nbn:de:swb:90-134338
KITopen-ID: 1000013433
Erschienen in Advances in Applied Probability
Band 40
Heft 2
Seiten 578-601
Schlagworte Cramér asymptotics; fluid limits; Lundberg coefficient; multidimensional birth processes; probability of ruin; risk reserve processes; urn models
Nachgewiesen in Scopus
Web of Science
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