The maximum surplus before ruin for two classes of perturbed risk model

Abstract

In this paper, we consider the distribution of the maximum surplus before ruin in a perturbed risk model with two independent classes of risks, in which both of the two inter-claim times have phase-type distributions. We obtain the integro-differential equations for the distribution of the maximum surplus before ruin. Explicit expressions are derived if the two classes claim amount distributions both belong to the rational family.

Keywords:

• Two classes of claims
• diffusion process
• maximum surplus before ruin
• phase-type distribution

AMS Subject Classifications:

• 62P05
• 91B30

Acknowledgements

The authors would like to thank the anonymous referee for his/her helpful comments and suggestions which improved the paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Project number 71371068], [Project number 71431008]; Humanities and Social Sciences Project of the Ministry Education in China [grant number 16YJA790015]; Hunan Provincial Academy of Social Sciences Fund of China [grant number 14YBA189]; China Postdoctoral Science Foundation [grant number 2015T80868], [grant number 2014M562105]; Hunan Provincial Natural Science Foundation of China [grant number 2015JJ4091]; Scientific Research Fund of Hunan Provincial Education Department of China [grant number 16A088].