Coupling and Explicit Rate of Convergence in Cramér–Lundberg Approximation for Reinsurance Risk Processes

Abstract

A classical result in risk theory is the Cramér–Lundberg approximation which says that under some general conditions the exponentially normalized ruin probability converges. In this article, we state an explicit rate of convergence for the Cramér–Lundberg approximation for ruin probabilities in the case where claims are bounded, which is realistic for, e.g., reinsurance models. The method, used to get the corresponding results, is based on renewal and coupling arguments.

Keywords:

• Coupling method
• Cramér-Lundberg approximation
• Rate of convergence
• Reinsurance risk process
• Reinsurance ruin probability

Mathematics Subject Classification:

• Primary 60K05, 60K10
• Secondary 62P05