Ruin probability and time of ruin with a proportional reinsurance threshold strategy |
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Authors: | Anna Casta?er M Mercè Claramunt Maite Mármol |
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Institution: | 1. Dept. Matem??tica Econ??mica, Financera i Actuarial, University of Barcelona, Av. Diagonal, 696, 08034, Barcelona, Spain
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Abstract: | 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?CShiu 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. |
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