We consider a Cramér-Lundberg insurance risk process with the added feature of reinsurance. If an arriving claim finds the reserve below a certain threshold γ, or if it would bring the reserve below that level, then a reinsurer pays part of the claim. Using fluctuation theory and the theory of scale functions of spectrally negative Lévy processes, we derive expressions for the Laplace transform of the time to ruin and of the joint distribution of the deficit at ruin and the surplus before ruin. We specify these results in much more detail for the threshold set-up in the case of proportional reinsurance.
Bibliographical noteFunding Information:
The research of David Perry was partially supported by the German-Israel Science Foundation (grant number 1-1184-31.4/2012) and the Israel Science Foundation (grant number 1071/14).
Copyright © 2017 Applied Probability Trust.
- Spectrally negative Lévy process
- claim refraction
- ruin probability
- scale function
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics (all)
- Statistics, Probability and Uncertainty