On a Joint Distribution for the Classical Risk Process with a Stochastic Return on Investments

Abstract

In this paper, we consider the classical risk process with a stochastic return on investments. We derive an explicit expression for the joint distribution of three important actuarial diagnostics: the time of ruin, the surplus immediately before ruin and deficit at ruin, which generalizes the corresponding result in Wu et al. ^[12] for the risk process with a constant force of interest.

Keywords:

• Classical risk process
• Joint distribution
• Markov skeleton process
• Stochastic return

Mathematics Subject Classification:

• Primary 60J75
• Secondary 91B30

ACKNOWLEDGMENTS

The authors would like to thank the anonymous referees and the editor for their valuable comments, helpful suggestions and correcting mistakes which lead to a great improvement of the earlier version of the paper.

This work was supported by the National Natural Science Foundation of China (NSFC grant No. 10571132 and 10571092).