Some results on ruin probabilities in a two-dimensional risk model

Ruin theory under multi-dimensional risk models is very complex. Even in the two-dimensional case, the problem is challenging. In this paper, we consider a bivariate risk model. Three different types of ruin probabilities are defined. Using some results of one-dimensional risk processes, simple boun...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2003-07, Vol.32 (3), p.345-358
Main Authors: Chan, Wai-Sum, Yang, Hailiang, Zhang, Lianzeng
Format: Article
Language:English
Subjects:
Adjustment coefficient
Asymptotic good bound
Coefficients
Economics
Insurance
Integral–differential equation
Mathematical analysis
Mathematical models
Mathematics
Model testing
Phase-type distribution
Probability
Probability of ruin
Risk
Risk assessment
Studies
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Summary:Ruin theory under multi-dimensional risk models is very complex. Even in the two-dimensional case, the problem is challenging. In this paper, we consider a bivariate risk model. Three different types of ruin probabilities are defined. Using some results of one-dimensional risk processes, simple bounds for the two-dimensional ruin probabilities are obtained. Numerical examples and simulation experiments are given to illustrate the tightness of the bounds. A partial integral–differential equation satisfied by the two-dimensional ruin probabilities is derived. Although special cases and examples in this paper provide some exciting results, the problem of ruin probability in a multi-dimensional risk model is still far from solved. We hope that this paper stimulates more research by actuaries in this area.
ISSN:0167-6687
1873-5959
DOI:10.1016/S0167-6687(03)00115-X