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Risks 2013, 1(2), 45-56; doi:10.3390/risks1020045

Optimal Reinsurance: A Risk Sharing Approach

1,* , 2
1 University Carlos III of Madrid. CL. Madrid 126. 28903 Getafe, Madrid, Spain 2 University of Castilla la Mancha Avda. Real Fábrica de Seda, s/n. 45600 Talavera, Toledo, Spain 3 University Complutense of Madrid. Department of Actuarial and Financial Economics. Somosaguas-Campus. 28223 Pozuelo de Alarcón, Madrid, Spain
* Author to whom correspondence should be addressed.
Received: 11 June 2013 / Revised: 21 July 2013 / Accepted: 24 July 2013 / Published: 5 August 2013
(This article belongs to the collection Systemic Risk and Reinsurance)
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This paper proposes risk sharing strategies, which allow insurers to cooperate and diversify non-systemic risk. We deal with both deviation measures and coherent risk measures and provide general mathematical methods applying to optimize them all. Numerical examples are given in order to illustrate how efficiently the non-systemic risk can be diversified and how effective the presented mathematical tools may be. It is also illustrated how the existence of huge disasters may lead to wrong solutions of our optimal risk sharing problem, in the sense that the involved risk measure could ignore the existence of a non-null probability of "global ruin" after the design of the optimal risk sharing strategy. To overcome this caveat, one can use more conservative risk measures. The stability in the large of the optimal sharing plan guarantees that "the global ruin caveat" may be also addressed and solved with the presented methods.
Keywords: optimal reinsurance; general risk measure; risk sharing; systemic risk optimal reinsurance; general risk measure; risk sharing; systemic risk
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Balbas, A.; Balbas, B.; Balbas, R. Optimal Reinsurance: A Risk Sharing Approach. Risks 2013, 1, 45-56.

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