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Stochastic cooperative games in insurance and reinsurance

Author

Listed:
  • Suijs, J.P.M.

    (Tilburg University, School of Economics and Management)

  • De Waegenaere, A.M.B.

    (Tilburg University, School of Economics and Management)

  • Borm, P.E.M.

    (Tilburg University, School of Economics and Management)

Abstract

This paper shows how problems in `non life'-insurance and `non life'-reinsurance can be modelled simultaneously as cooperative games with stochastic payoffs.Pareto optimal allocations of the risks faced by the insurers and the insureds are determined.It is shown that the core of the corresponding insurance games is nonempty.Moreover, it is shown that specific core allocations are obtained when the zero utility principle is used for calculating premiums. Finally, game theory is used to give a justification for subadditive premiums.
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Suggested Citation

  • Suijs, J.P.M. & De Waegenaere, A.M.B. & Borm, P.E.M., 1998. "Stochastic cooperative games in insurance and reinsurance," Other publications TiSEM 01f181bb-862a-4712-9204-9, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:01f181bb-862a-4712-9204-91ca9d7896f5
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    References listed on IDEAS

    as
    1. Suijs, Jeroen & Borm, Peter & De Waegenaere, Anja & Tijs, Stef, 1999. "Cooperative games with stochastic payoffs," European Journal of Operational Research, Elsevier, vol. 113(1), pages 193-205, February.
    2. Alegre, Antoni & Claramunt, M. Merce, 1995. "Allocation of solvency cost in group annuities: Actuarial principles and cooperative game theory," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 19-34, August.
    3. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    4. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
    5. Borch, Karl, 1962. "Application of Game Theory to Some Problems in Automobile Insurance*)," ASTIN Bulletin, Cambridge University Press, vol. 2(2), pages 208-221, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Suijs, J.P.M., 1999. "Insurance Games," Discussion Paper 1999-95, Tilburg University, Center for Economic Research.
    2. Stefan Thurner & Rudolf Hanel & Stefan Pichler, 2003. "Risk trading, network topology and banking regulation," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 306-319.
    3. Suijs, J.P.M., 1998. "Cooperative decision making in a stochastic environment," Other publications TiSEM a84d779a-d5a9-48e9-bfe7-4, Tilburg University, School of Economics and Management.
    4. J. Puerto & F. Fernández & Y. Hinojosa, 2008. "Partially ordered cooperative games: extended core and Shapley value," Annals of Operations Research, Springer, vol. 158(1), pages 143-159, February.
    5. Taksar, Michael & Zeng, Xudong, 2011. "Optimal non-proportional reinsurance control and stochastic differential games," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 64-71, January.
    6. Andreas Tsanakas & Evangelia Desli, 2005. "Measurement and Pricing of Risk in Insurance Markets," Risk Analysis, John Wiley & Sons, vol. 25(6), pages 1653-1668, December.
    7. Suijs, J.P.M., 1999. "Price Uncertainty in Linear Production Situations," Other publications TiSEM 7e9b38b7-5b6c-4f12-86c8-8, Tilburg University, School of Economics and Management.
    8. Donald Nganmegni Njoya & Issofa Moyouwou & Nicolas Gabriel Andjiga, 2021. "The equal-surplus Shapley value for chance-constrained games on finite sample spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 463-499, June.
    9. Zuofeng Gao & Hongxin Bai & Suting Zhang & Yongbo Yu & Chunyan Han & Hua Zhang, 2008. "The -Core of a -person Stochastic Cooperative Game," Modern Applied Science, Canadian Center of Science and Education, vol. 2(2), pages 1-71, March.
    10. Asimit, Vali & Boonen, Tim J., 2018. "Insurance with multiple insurers: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 778-790.
    11. Jin, Zhuo & Yin, G. & Wu, Fuke, 2013. "Optimal reinsurance strategies in regime-switching jump diffusion models: Stochastic differential game formulation and numerical methods," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 733-746.
    12. Suijs, J.P.M., 1999. "Insurance Games," Other publications TiSEM 8d27bea0-5898-48ea-bd53-7, Tilburg University, School of Economics and Management.
    13. Suijs, J.P.M., 1999. "Price Uncertainty in Linear Production Situations," Discussion Paper 1999-91, Tilburg University, Center for Economic Research.
    14. Laszlo A. Koczy, 2019. "The risk-based core for cooperative games with uncertainty," CERS-IE WORKING PAPERS 1906, Institute of Economics, Centre for Economic and Regional Studies.
    15. Zeng, Xudong & Luo, Shangzhen, 2013. "Stochastic Pareto-optimal reinsurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 671-677.

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