On a ruin model with both interclaim times and premiums depending on claim sizes

Abstract

Under the classical compound Poisson risk model and the Sparre-Andersen risk model, one crucial assumption is that the interclaim times and the claim sizes are independent. However, this assumption might be inappropriate in practice. In this paper, we consider a continuous-time risk process where the interclaim-time distribution and premium rate both depend on the size of the previous claim. Explicit solutions for the Gerber–Shiu discounted penalty function with arbitrary claim-size distribution are derived utilizing the roots of a generalized Lundberg’s equation. Applications with exponential thresholds and -family claim sizes are presented. A numerical example is provided.