Details
| Original language | English |
|---|---|
| Pages (from-to) | 379-408 |
| Number of pages | 30 |
| Journal | Astin bulletin |
| Volume | 35 |
| Issue number | 2 |
| Publication status | Published - Nov 2005 |
Abstract
Multivariate stochastic processes with Poisson marginals are of interest in insurance and finance; they can be used to model the joint behaviour of several claim arrival processes, for example. We discuss various methods for the construction of such models, with particular emphasis on the use of copulas. An important class of multivariate counting processes with Poisson marginals arises if the events of a background Poisson process with constant intensity are moved forward in time by a random amount and possibly deleted; here we think of the events of the background process as triggering later claims in different categories. We discuss structural aspects of these models, their dependence properties together with stochastic order aspects, and also some related computational issues. Various actuarial applications are indicated.
Keywords
- Claim arrival processes, dependency, point processes, Poisson processes, stochastic modelling, stochastic ordering
ASJC Scopus subject areas
- Business, Management and Accounting(all)
- Accounting
- Economics, Econometrics and Finance(all)
- Finance
- Economics, Econometrics and Finance(all)
- Economics and Econometrics
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In: Astin bulletin, Vol. 35, No. 2, 11.2005, p. 379-408.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Multivariate Counting Processes
T2 - Copulas and Beyond
AU - Bäuerle, Nicole
AU - Grübel, Rudolf
PY - 2005/11
Y1 - 2005/11
N2 - Multivariate stochastic processes with Poisson marginals are of interest in insurance and finance; they can be used to model the joint behaviour of several claim arrival processes, for example. We discuss various methods for the construction of such models, with particular emphasis on the use of copulas. An important class of multivariate counting processes with Poisson marginals arises if the events of a background Poisson process with constant intensity are moved forward in time by a random amount and possibly deleted; here we think of the events of the background process as triggering later claims in different categories. We discuss structural aspects of these models, their dependence properties together with stochastic order aspects, and also some related computational issues. Various actuarial applications are indicated.
AB - Multivariate stochastic processes with Poisson marginals are of interest in insurance and finance; they can be used to model the joint behaviour of several claim arrival processes, for example. We discuss various methods for the construction of such models, with particular emphasis on the use of copulas. An important class of multivariate counting processes with Poisson marginals arises if the events of a background Poisson process with constant intensity are moved forward in time by a random amount and possibly deleted; here we think of the events of the background process as triggering later claims in different categories. We discuss structural aspects of these models, their dependence properties together with stochastic order aspects, and also some related computational issues. Various actuarial applications are indicated.
KW - Claim arrival processes
KW - dependency
KW - point processes
KW - Poisson processes
KW - stochastic modelling
KW - stochastic ordering
UR - http://www.scopus.com/inward/record.url?scp=85011476706&partnerID=8YFLogxK
U2 - 10.1017/S0515036100014306
DO - 10.1017/S0515036100014306
M3 - Article
AN - SCOPUS:85011476706
VL - 35
SP - 379
EP - 408
JO - Astin bulletin
JF - Astin bulletin
SN - 0515-0361
IS - 2
ER -