A surplus process involving a compound Poisson counting process and applications

Abstract

In this paper, we introduce a surplus process involving a compound Poisson counting process, which is a generalization of the classical ruin model where the claim-counting process is a homogeneous Poisson process. The incentive is to model batch arrival of claims using a counting process that is based on a compound distribution. This reduces the difficulty of modeling claim amounts and is consistent with industrial data. Recursive formula, some properties and relevant main ruin theory results are provided. Further, we consider applications involving zero-truncated negative binomial and zero-truncated binomial batch arrivals when the claim amounts follow exponential or Erlang distribution.

Keywords:

• batch claim arrivals
• compound Poisson process
• Gerber-Shiu function
• Heaviside Expansion Theorem
• ruin theory

Acknowledgments

The authors want to thank an anonymous referee for a thorough read of an earlier version of the paper and for insightful comments.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC).