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The Effect of a threshold proportional reinsurance strategy on ruin probabilities
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[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.
[eng] In the context of a compound Poisson risk model, we define a threshold proportional reinsurance strategy: A retention level k1 is applied whenever the reserves are less than a determinate threshold b, and a retention level k2 is applied in the other case. We obtain the integro-differential equation for the Gerber-Shiu function, defined in Gerber and Shiu -1998-, in this model, which allows us to obtain the expressions for ruin probability and Laplace transforms of time of ruin for several distributions of the claim sizes. Finally, we present some numerical results.
[eng] In the context of a compound Poisson risk model, we define a threshold proportional reinsurance strategy: A retention level k1 is applied whenever the reserves are less than a determinate threshold b, and a retention level k2 is applied in the other case. We obtain the integro-differential equation for the Gerber-Shiu function, defined in Gerber and Shiu -1998-, in this model, which allows us to obtain the expressions for ruin probability and Laplace transforms of time of ruin for several distributions of the claim sizes. Finally, we present some numerical results.
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CASTAÑER, Anna, CLARAMUNT BIELSA, M. Mercè and MÁRMOL, Maite. The Effect of a threshold proportional reinsurance strategy on ruin probabilities. Documents de treball (Facultat d'Economia i Empresa. Espai de Recerca en Economia). 2009. Vol. E09/222. ISSN 1136-8365. [consulted: 3 of August of 2026]. Available at: https://hdl.handle.net/2445/43646