Publication: Optimal reinsurance under risk and uncertainty
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2014-06-01
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Abstract
This paper deals with the optimal reinsurance problem if both insurer and
reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also
included. The insurer and reinsurer degrees of uncertainty do not have to be identical.
The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to
the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the
reinsurer moral hazard is totally eliminated.
Three main contributions seem to be reached. Firstly, necessary and sufficient opti-
mality conditions are given. Secondly, the optimal contract is often a bang-bang solution,
i:e:, the sensitivity between the retained risk and the total claims saturates the imposed
constraints. For some special cases the optimal contract might not be bang-bang, but there
is always a bang-bang contract as close as desired to the optimal one. Thirdly, the optimal
reinsurance problem is equivalent to other linear programming problem, despite the fact
that risk, uncertainty, and many premium principles are not linear. This may be impor-
tant because linear problems are easy to solve in practice, since there are very efficient
algorithms.
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Keywords
Risk and uncertainty, Moral Hazard, Optimal Reinsurance and Optimality Conditions, Bang-Bang Solution, The Optimal Reinsurance Linear Problem