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Title: Some optimization and decision problems in proportional reinsurance
Author: Castañer, Anna
Claramunt Bielsa, M. Mercè
Mármol, Maite
Keywords: Reassegurances
Gestió del risc
Matemàtica financera
Risc (Assegurances)
Equacions diferencials
Risk management
Business mathematics
Risk (Insurance)
Differential equations
Issue Date: 2016
Publisher: ASEPUMA
Abstract: Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance strategy. To this end, we use as decision tools not only the probability of ruin but also the random variable deficit at ruin if ruin occurs. The discounted penalty function is employed to calculate as particular cases the probability of ruin and the moments and the distribution function of the deficit at ruin if ruin occurs. We consider the classical risk theory model assuming a Poisson process and an individual claim amount phase-type distributed, modified with a proportional reinsurance with a retention level that is not constant and depends on the level of the surplus. Depending on whether the initial surplus is below or above a threshold level, the discounted penalty function behaves differently. General expressions for this discounted penalty function are obtained, as well as interesting theoretical results and explicit expressions for phase-type 2 distribution. These results are applied in numerical examples of decision problems based on the probability of ruin and on different risk measures of the deficit at ruin if ruin occurs (the expectation, the Value at Risk and the Tail Value at Risk).
Note: Reproducció del document publicat a:
It is part of: Rect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA, 2016, vol. 17, num. 1, p. 35-55
ISSN: 1575-605X
Appears in Collections:Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)

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