Dependence properties and bounds for ruin probabilities in multivariate compound risk models
In risk management, ignoring the dependence among various types of claims often results in over-estimating or under-estimating the ruin probabilities of a portfolio. This paper focuses on three commonly used ruin probabilities in multivariate compound risk models, and using the comparison methods shows how some ruin probabilities increase, whereas the others decrease, as the claim dependence grows. The paper also presents some computable bounds for these ruin probabilities, which can be calculated explicitly for multivariate phase-type distributed claims, and illustrates the performance of these bounds for the multivariate compound Poisson risk models with slightly or highly dependent Marshall-Olkin exponential claim sizes.
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Volume (Year): 98 (2007)
Issue (Month): 4 (April)
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- 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.
- Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
- Sundt, Bjørn, 1999. "On Multivariate Panjer Recursions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 29(01), pages 29-45, May.