Stability of the optimal reinsurance with respect to the risk measure

Beatriz Balbás and Antonio Heras

DEE - Working Papers. Business Economics. WB from Universidad Carlos III de Madrid. Departamento de Economía de la Empresa

Abstract: The optimal reinsurance problem is a classic topic in Actuarial Mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advantages and shortcomings when compared with others. This paper deals with a discrete probability space and analyzes the stability of the optimal reinsurance with respect to the risk measure that the insurer uses. We will demonstrate that there is a “stable optimal retention” that will show no sensitivity, insofar as it will solve the optimal reinsurance problem for many risk measures, thus providing a very robust reinsurance plan. This stable optimal retention is a stop-loss contract, and it is easy to compute in practice. A fast algorithm will be given and a numerical example presented.

Keywords: Optimal; reinsurance; Risk; measure; Sensitivity; Stable; optimal; retention; Stop-loss; reinsurance (search for similar items in EconPapers)
JEL-codes: G11 G22 (search for similar items in EconPapers)
Date: 2010-01
New Economics Papers: this item is included in nep-ias and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wbrepe:wb100201

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