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# Probability of ruin for a dependent, two-dimensional Poisson process

## Author

Listed:
• Stanisław Heilpern

## Abstract

A two-dimensional, dependent Poisson risk process is investigated in the paper. Claims are divided into two classes. Within each class claims have the same distribution, but claims belonging to different classes can have different distributions and the corresponding counting processes can be dependent. This dependence is induced by a common factor. Three models of ruin and the probabilities of ruin are investigated. The influence of the degree of class dependence on the probability of ruin are studied for each model.

## Suggested Citation

• Stanisław Heilpern, 2009. "Probability of ruin for a dependent, two-dimensional Poisson process," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(1), pages 77-90.
• Handle: RePEc:wut:journl:v:1:y:2009:p:77-90
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## References listed on IDEAS

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1. Chan, Wai-Sum & Yang, Hailiang & Zhang, Lianzeng, 2003. "Some results on ruin probabilities in a two-dimensional risk model," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 345-358, July.
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## More about this item

### Keywords

Poisson process; claim; model of ruin; simulation; phase-type distribution;
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