Publication: Stability of the optimal reinsurance with respect to the risk measure
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2010-01
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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.
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Optimal reinsurance, Risk measure, Sensitivity, Stable optimal retention, Stop-loss reinsurance