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Optimal Reinsurance: A Risk Sharing Approach

Author

Listed:
  • Alejandro Balbas

    (University Carlos III of Madrid. CL. Madrid 126. 28903 Getafe, Madrid, Spain)

  • Beatriz Balbas

    (University of Castilla la Mancha Avda. Real Fábrica de Seda, s/n. 45600 Talavera, Toledo, Spain)

  • Raquel Balbas

    (University Complutense of Madrid. Department of Actuarial and Financial Economics. Somosaguas-Campus. 28223 Pozuelo de Alarcón, Madrid, Spain)

Abstract

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.

Suggested Citation

  • Alejandro Balbas & Beatriz Balbas & Raquel Balbas, 2013. "Optimal Reinsurance: A Risk Sharing Approach," Risks, MDPI, vol. 1(2), pages 1-12, August.
    • Handle: RePEc:gam:jrisks:v:1:y:2013:i:2:p:45-56:d:27724
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    References listed on IDEAS

    as
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    2. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
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    7. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 374-384, June.
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    9. Kaluszka, Marek, 2005. "Optimal reinsurance under convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 375-398, June.
    10. Cai, Jun & Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2008. "Optimal reinsurance under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 185-196, August.
    11. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
    12. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

    1. Sancho Salcedo-Sanz & Leo Carro-Calvo & Mercè Claramunt & Ana Castañer & Maite Mármol, 2014. "Effectively Tackling Reinsurance Problems by Using Evolutionary and Swarm Intelligence Algorithms," Risks, MDPI, vol. 2(2), pages 1-14, April.
    2. Massimiliano Kaucic & Roberto Daris, 2015. "Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints," Risks, MDPI, vol. 3(3), pages 1-30, September.

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