Ruin Probabilities in a Risk Model with Two Types of Claims
- Authors
- 한지연; 최승경; 이의용
- Issue Date
- Oct-2012
- Publisher
- 한국통계학회
- Keywords
- Continuous time risk model; surplus process with two types of claims; ruin probability; integro-differential equation.
- Citation
- 응용통계연구, v.25, no.5, pp 813 - 820
- Pages
- 8
- Journal Title
- 응용통계연구
- Volume
- 25
- Number
- 5
- Start Page
- 813
- End Page
- 820
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/12125
- DOI
- 10.5351/KJAS.2012.25.5.813
- ISSN
- 1225-066X
- 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.
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