On the stop-loss transform and order for the surplus process perturbed by diffusion
详细信息 查看全文
- 作者：Cary Chi-Liang Tsai
- 关键词：Surplus process ; Diffusion process ; Ruin probability ; Maximal aggregate loss ; Compound geometric distribution ; Stop-loss transform ; Ordering
- 刊名：Insurance: Mathematics and Economics
- 出版年：2006
- 出版时间：1 August 2006
- 年：2006
- 卷：39
- 期：1
- 页码：151-170
- 全文大小：837 K
文摘
In this paper we extend the results obtained in [Chang, Y., Pai, J.S., 2003. On the nth stop-loss transform order of ruin probability. Insurance: Mathematics and Economics 32, 51–60] to ones based on the surplus process perturbed by diffusion. We first study the stop-loss transforms of the random variables for the maximal aggregate loss. Then we propose theorems for the order of stop-loss transforms of ruin probabilities for two surplus processes perturbed by diffusion associated with different claim size random variables of same mean. We also find that an exponentially distributed random variable is less, in the meaning of the first stop-loss order, than a mixture of two exponentials with the same mean. Finally, a numerical example is given to illustrate these theorems.