Stability of the optimal reinsurance with respect to the risk measure
AbstractThe 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.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Economía de la Empresa in its series Business Economics Working Papers with number wb100201.
Date of creation: Jan 2010
Date of revision:
Optimal reinsurance; Risk measure; Sensitivity; Stable optimal retention; Stop-loss reinsurance;
Find related papers by JEL classification:
- G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-01-30 (All new papers)
- NEP-IAS-2010-01-30 (Insurance Economics)
- NEP-RMG-2010-01-30 (Risk Management)
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