Ruin probability and time of ruin with a proportional reinsurance threshold strategy

In this paper, we present a threshold proportional reinsurance strategy and we analyze the effect on some solvency measures: ruin probability and time of ruin. This dynamic reinsurance strategy assumes a retention level that is not constant and depends on the level of the surplus. In a model with inter‐occurrence times being generalized Erlang(n)‐distributed, we obtain the integro‐differential equation for the Gerber–Shiu function. Then, we present the solution for inter‐occurrence times exponentially distributed and claim amount phase‐type(N). Some examples for exponential and phase‐type(2) claim amount are presented. Finally, we show some comparisons between threshold reinsurance and proportional reinsurance.