Analysis of risk models using a level crossing technique

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.