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

Wai-sum Chan*, Hailiang Yang, Lianzeng Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

72 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)345-358
Number of pages14
JournalInsurance: Mathematics and Economics
Issue number3
Publication statusPublished - 21 Jul 2003
Externally publishedYes


  • Adjustment coefficient
  • Asymptotic good bound
  • Integral-differential equation
  • Phase-type distribution
  • Probability of ruin


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