Bounds for the Ruin Probability in the Sparre–Andersen Model

Abstract

We obtain the upper and lower bounds for the ruin probability in the Sparre–Andersen model. These bounds are established under various conditions: when the adjustment coefficient exists, when it does not exist, and when the interarrival distribution belongs to certain aging classes. Additionally, we improve the Lundberg upper bound for the ruin probability.

Keywords

• Sparre–Andersen model
• ruin probability
• truncated Cramer–Lundberg condition
• aging properties