Journal article
Multivariate risk model of phase type
Insurance, mathematics & economics, Vol.36(2), pp.137-152
2005
Handle:
https://hdl.handle.net/2376/113398
Abstract
This paper is concerned with several types of ruin probabilities for a multivariate compound Poisson risk model, where the claim size vector follows a multivariate phase type distribution. First, an explicit representation for the convolution of a multivariate phase type distribution is derived, and then an explicit formula for the ruin probability that the total claim surplus exceeds the total initial reserve in infinite horizon is obtained. Furthermore, the effect of the dependence among various types of claims on this type of ruin probability is considered under the convex and supermodular orders. In addition, the bounds for other types of ruin probabilities are developed by utilizing the association of multivariate phase type distributions. Finally, some examples are presented to illustrate the results.
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Details
- Title
- Multivariate risk model of phase type
- Creators
- Jun Cai - Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1Haijun Li - Department of Mathematics, Washington State University, Pullman, WA 99164, USA
- Publication Details
- Insurance, mathematics & economics, Vol.36(2), pp.137-152
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- Elsevier B.V
- Identifiers
- 99900547623801842
- Language
- English
- Resource Type
- Journal article