Analysis of risk models using a level crossing technique

作者：Brill Percy H^*; Yu Kaiqi

来源：Insurance: Mathematics and Economics , 2011, 49(3): 298-309.

DOI：10.1016/j.insmatheco.2011.05.005

• Dividend barrier or threshold
• Time until ruin
• Deficit at ruin
• Heavy-tailed claim sizes
• Hyperexponential claim sizes
• Level crossing method

This paper analyzes ruin-like risk models in Insurance, which are variants of the Cramer-Lundberg (C-L) model with a barrier or a threshold. We consider three model variants, which have different portfolio strategies when the risk reserve reaches the barrier or exceeds the threshold. In these models we construct a time-extended risk process defined on cycles of a specific renewal process. The time until ruin is equal to one cycle of the specific renewal process. We also consider a fourth model, which is a variant of a model proposed by Dickson and Waters (2004). The analysis of each model employs a level crossing method (LC) to derive the steady-state probability distribution of the time-extended risk process. From the derived distribution we compute the expected time until ruin, the probability distribution of the deficit at ruin, and related quantities of interest.

• 出版日期2011-11