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

Anna Castañer ^[1] ; M. Mercè Claramunt ^[1] ; Maite Mármol ^[1]
1. [1] Universitat de Barcelona
  
  Universitat de Barcelona
  
  Barcelona, España
Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 20, Nº. 3, 2012, págs. 614-638
Idioma: inglés
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Resumen
- 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.