Details
| Original language | English |
|---|---|
| Pages (from-to) | 578-601 |
| Number of pages | 24 |
| Journal | Advances in applied probability |
| Volume | 40 |
| Issue number | 2 |
| Publication status | Published - Jun 2008 |
Abstract
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.
Keywords
- Cramér asymptotic, Fluid limit, Lundberg coefficient, Multidimensional birth process, Probability of ruin, Risk reserve process, Urn model
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Applied Mathematics
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In: Advances in applied probability, Vol. 40, No. 2, 06.2008, p. 578-601.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Multivariate risk processes with interacting intensities
AU - Bäuerle, Nicole
AU - Grübel, Rudolf
PY - 2008/6
Y1 - 2008/6
N2 - 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.
AB - 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.
KW - Cramér asymptotic
KW - Fluid limit
KW - Lundberg coefficient
KW - Multidimensional birth process
KW - Probability of ruin
KW - Risk reserve process
KW - Urn model
UR - http://www.scopus.com/inward/record.url?scp=49449107342&partnerID=8YFLogxK
U2 - 10.1239/aap/1214950217
DO - 10.1239/aap/1214950217
M3 - Article
AN - SCOPUS:49449107342
VL - 40
SP - 578
EP - 601
JO - Advances in applied probability
JF - Advances in applied probability
SN - 0001-8678
IS - 2
ER -