Total Duration of Negative Surplus for the Risk Process with Constant Interest Force

Abstract

Assuming the compound Poisson risk process with constant interest force, we consider the process as continuing if ruin occurs. We introduce the renewal measure of the defective renewal sequence constituted by the zero points of the surplus process. The density functions of this renewal measure and the first-hitting time of the zero point are derived. By these density functions together with the strong Markov property of the surplus process, we obtain the explicit expression for the total duration of negative surplus.

Keywords:

• Compound Poisson risk process
• First-hitting time
• Interest
• Renewal measure
• Strong Markov property
• Total duration of negative surplus

Mathematics Subject Classification:

• Primary 91B30
• Secondary 60J60

The authors would like to express particular thanks to the anonymous referee for helpful comments and suggestions, which have improved the presentation of the whole article. This research is supported by NNSF (Grant No.10571092) of China and the Research Fund for the Doctorial Program of Higher Education.