The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Ruin Probabilities in a Risk Model with Two Types of Claims

  • Han, Ji-Yeon (Department of Statistics, Sookmyung Women's University) ;
  • Choi, Seung-Kyoung (Department of Statistics, Sookmyung Women's University) ;
  • Lee, Eui-Yong (Department of Statistics, Sookmyung Women's University)
  • Received : 2012.06.12
  • Accepted : 2012.08.28
  • Published : 2012.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

A surplus process with two types of claims is considered, where Type I claims occur more frequently, however, their sizes are smaller stochastically than Type II claims. The ruin probabilities of the surplus caused by each type of claim are obtained by establishing integro-differential equations for the ruin probabilities. The formulas of the ruin probabilities contain an infinite sum and convolutions that make the formulas hard to be applicable in practice; subsequently, we obtain explicit formulas for the ruin probabilities when the sizes of both types of claims are exponentially distributed. Finally, we show through a numerical example, that Type II claims have more impact on the ruin probability of the surplus than Type I claims.

Keywords

References

  1. Chan, W. S., Yang, H. and Zhang, L. (2003). Some results on ruin probabilities in a two-dimensional risk model, Insurance: Mathematics & Economics, 32, 345-358. https://doi.org/10.1016/S0167-6687(03)00115-X
  2. Dufresne, F. and Gerber, H. U. (1991). Risk theory for the compound Poisson process that is perturbed by diffusion, Insurance: Mathematics & Economics, 10, 51-59. https://doi.org/10.1016/0167-6687(91)90023-Q
  3. Grandell, J. (2000). Simple approximations of the ruin probabilities, Insurance: Mathematics and Economics, 26, 157-173. https://doi.org/10.1016/S0167-6687(99)00050-5
  4. uo, J. Y., Yuen, K. C. and Zhou, M. (2007). Ruin probabilities in Cox risk models with two dependent classes of business, Acta Mathematica Sinica, English Series, 23, 1281-1288. https://doi.org/10.1007/s10114-005-0819-7
  5. Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004). Loss Model: From Data to Decisions, 2nd ed, John Wiley & Sons, Hoboken.
  6. Li, S. and Garrido, J. (2005). Ruin probabilities for two classes of risk processes, ASTIN Bulletin, 35, 61-77. https://doi.org/10.2143/AST.35.1.583166
  7. Lv, T. L., Guo, J. Y. and Zhang, X. (2010). Ruin probabilities for a risk model with two classes of claims, Acta Mathematica Sinica, English Series, 26, 1749-1760. https://doi.org/10.1007/s10114-010-8091-x
  8. Tsai, C. C. L. (2009). On the ordering of ruin probabilities for the surplus process perturbed by diffusion, Scandinavian Actuarial Journal, 2009, 187-204. https://doi.org/10.1080/03461230801980417