On the first time of ruin in the bivariate compound Poisson model

This paper considers a bivariate compound Poisson model for a book of two dependent classes of insurance business. We focus on the ruin probability that at least one class of business will get ruined. As expected, general explicit expressions for this bivariate ruin probability is very difficult to...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2006-04, Vol.38 (2), p.298-308
Main Authors: Yuen, Kam C., Guo, Junyi, Wu, Xueyuan
Format: Article
Language:English
Subjects:
Association property
Compound binomial
Compound Poisson
Financial economics
Insurance
Mathematical economics
Orthant order
Poisson distribution
Probability
Ruin probability
Stochastic models
Stochastic processes
Studies
Survival probability
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Summary:This paper considers a bivariate compound Poisson model for a book of two dependent classes of insurance business. We focus on the ruin probability that at least one class of business will get ruined. As expected, general explicit expressions for this bivariate ruin probability is very difficult to obtain. In view of this, we introduce the so-called bivariate compound binomial model which can be used to approximate the finite-time survival probability of the assumed model. We then study some simple bounds for the infinite-time ruin probability via the association properties of the bivariate compound Poisson model. We also investigate the impact of dependence on the infinite-time ruin probability by means of multivariate stochastic orders.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2005.08.011