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Insurance Markets and Companies
Article . 2010
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Deficit at ruin with threshold proportional reinsurance

Authors: Castañer, Anna; Claramunt Bielsa, M. Mercè; Mármol, Maite;

Deficit at ruin with threshold proportional reinsurance

Abstract

In this paper, we focus our analysis on the distribution function and the moments of the deficit at ruin in a model with a threshold proportional reinsurance strategy using the Gerber-Shiu function. This strategy considers a proportional reinsurance, but the retention level is not constant and depends on the surplus. Then a retention level k1 is applied whenever the surplus is less than a specific threshold b, and a retention level k2 is applied in the other case. In a Poisson risk model, we derive the integro-differential equation for the Gerber-Shiu function when the claim amount is exponentially distributed. Then, we obtain the analytical expression for the Gerber-Shiu function for a set of penalty functions. This analytical expression is applicable for several penalty functions and includes, among others, the ruin probability, the time of ruin and the distribution function of the deficit at ruin.

Country
Spain
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Keywords

Differential equations, Insurance, Business mathematics, Risk management, Reinsurance, HG8011-9999, Matemàtica financera, Equacions diferencials, Reassegurances, Gestió del risc

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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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