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Optimal reinsurance under risk and uncertainty

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Balbás, Alejandro and Balbás, Beatriz and Balbás Aparicio, Raquel and Heras Martínez, Antonio José (2014) Optimal reinsurance under risk and uncertainty. [ ]

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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 optimality conditions are given in a very general setting. 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. 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 important because linear problems may be easily solved in practice, since there are very efficient algorithms.


Item Type:Working Paper or Technical Report
Additional Information:

Publicado también como artículo: Balbás, A.; Balbás, B.; Balbás, R.; Heras, A. (2015) "Optimal reinsurance under risk and uncertainty" Insurance: Mathematics and Economics, vol. 60, pages 61-74. ISSN: 01676687 http://dx.doi.org/10.1016/j.insmatheco.2014.11.001

Uncontrolled Keywords:Risk and uncertainty; Moral hazard; Optimal reinsurance and optimality conditions; Bang–bang solution; The optimal reinsurance linear problem
Subjects:Social sciences > Economics > Insurance
JEL:G22
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ID Code:60914
Deposited On:15 Jun 2020 17:17
Last Modified:17 Jun 2020 15:43

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