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Allocation of risks and equilibrium in markets with finitely many traders

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  • Burgert, Christian
  • Rüschendorf, Ludger

Abstract

The optimal risk allocation problem, equivalently the optimal risk sharing problem, in a market with n traders endowed with risk measures [varrho]1,...,[varrho]n is a classical problem in insurance and mathematical finance. This problem however only makes sense under a condition motivated from game theory which is called Pareto equilibrium. There are many situations of practical interest, where this condition does not hold. This is the case if the risk measures are based on essential different views towards risk. In this paper we introduce and analyze a meaningful extension of the optimal risk allocation (risk sharing) problem without assuming the equilibrium condition. The main point of this is to introduce a suitable and well motivated restriction on the class of admissible allocations which prevents effects of artificial [`]risk arbitrage'. As a result we obtain a new coherent risk measure which describes the inherent risk which remains after using admissible risk exchange in an optimal way.

Suggested Citation

  • Burgert, Christian & Rüschendorf, Ludger, 2008. "Allocation of risks and equilibrium in markets with finitely many traders," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 177-188, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:177-188
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    References listed on IDEAS

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    Cited by:

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    3. Grechuk, Bogdan, 2015. "The center of a convex set and capital allocation," European Journal of Operational Research, Elsevier, vol. 243(2), pages 628-636.
    4. Matteo Burzoni & Cosimo Munari & Ruodu Wang, 2020. "Adjusted Expected Shortfall," Papers 2007.08829, arXiv.org, revised Aug 2021.
    5. Mao, Tiantian & Hu, Jiuyun & Liu, Haiyan, 2018. "The average risk sharing problem under risk measure and expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 170-179.
    6. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2024. "Inf-convolution and optimal risk sharing with countable sets of risk measures," Annals of Operations Research, Springer, vol. 336(1), pages 829-860, May.
    7. Kiesel Swen & Rüschendorf Ludger, 2014. "Optimal risk allocation for convex risk functionals in general risk domains," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 335-365, December.
    8. Burzoni, Matteo & Munari, Cosimo & Wang, Ruodu, 2022. "Adjusted Expected Shortfall," Journal of Banking & Finance, Elsevier, vol. 134(C).
    9. Michail Anthropelos & Gordan Zitkovic, 2009. "Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability," Papers 0901.3318, arXiv.org.
    10. Li, Peng & Lim, Andrew E.B. & Shanthikumar, J. George, 2010. "Optimal risk transfer for agents with germs," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 1-12, August.
    11. Bogdan Grechuk & Michael Zabarankin, 2012. "Optimal risk sharing with general deviation measures," Annals of Operations Research, Springer, vol. 200(1), pages 9-21, November.
    12. Deng, Qianli & Jiang, Xianglin & Cui, Qingbin & Zhang, Limao, 2015. "Strategic design of cost savings guarantee in energy performance contracting under uncertainty," Applied Energy, Elsevier, vol. 139(C), pages 68-80.
    13. Kiesel Swen & Rüschendorf Ludger, 2009. "Characterization of optimal risk allocations for convex risk functionals," Statistics & Risk Modeling, De Gruyter, vol. 26(4), pages 303-319, July.
    14. Grechuk, Bogdan, 2023. "Extended gradient of convex function and capital allocation," European Journal of Operational Research, Elsevier, vol. 305(1), pages 429-437.
    15. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 426-433, June.

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