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Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures

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  • Mario Ghossoub
  • Michael B. Zhu
  • Wing Fung Chong

Abstract

We study Pareto optimality in a decentralized peer-to-peer risk-sharing market where agents' preferences are represented by robust distortion risk measures that are not necessarily convex. We obtain a characterization of Pareto-optimal allocations of the aggregate risk in the market, and we show that the shape of the allocations depends primarily on each agent's assessment of the tail of the aggregate risk. We quantify the latter via an index of probabilistic risk aversion, and we illustrate our results using concrete examples of popular families of distortion functions. As an application of our results, we revisit the market for flood risk insurance in the United States. We present the decentralized risk sharing arrangement as an alternative to the current centralized market structure, and we characterize the optimal allocations in a numerical study with historical flood data. We conclude with an in-depth discussion of the advantages and disadvantages of a decentralized insurance scheme in this setting.

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  • Mario Ghossoub & Michael B. Zhu & Wing Fung Chong, 2024. "Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures," Papers 2409.05103, arXiv.org.
    • Handle: RePEc:arx:papers:2409.05103
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    References listed on IDEAS

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    1. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    2. repec:dau:papers:123456789/5393 is not listed on IDEAS
    3. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    4. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    5. Marc Oliver Rieger & Mei Wang & Thorsten Hens, 2017. "Estimating cumulative prospect theory parameters from an international survey," Theory and Decision, Springer, vol. 82(4), pages 567-596, April.
    6. Wei Wang & Huifu Xu, 2023. "Preference robust distortion risk measure and its application," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 389-434, April.
    7. Tim J. Boonen & Fangda Liu & Ruodu Wang, 2021. "Competitive equilibria in a comonotone market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1217-1255, November.
    8. Liu, Haiyan, 2020. "Weighted Comonotonic Risk Sharing Under Heterogeneous Beliefs," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 647-673, May.
    9. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Post-Print halshs-00470670, HAL.
    10. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    11. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    12. repec:dau:papers:123456789/2348 is not listed on IDEAS
    13. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    14. 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.
    15. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    16. Michel Denuit & Jan Dhaene & Christian Y. Robert, 2022. "Risk‐sharing rules and their properties, with applications to peer‐to‐peer insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(3), pages 615-667, September.
    17. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    18. Guillaume Carlier & Rose-Anne Dana, 2003. "Pareto efficient insurance contracts when the insurer's cost function is discontinuous," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 871-893, June.
    19. Ghossoub, Mario & Zhu, Michael B., 2024. "Stackelberg equilibria with multiple policyholders," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 189-201.
    20. Amarante, Massimiliano & Ghossoub, Mario & Phelps, Edmund, 2015. "Ambiguity on the insurer’s side: The demand for insurance," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 61-78.
    21. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    22. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    23. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2016. "The role of a representative reinsurer in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 196-204.
    24. Cui, Wei & Yang, Jingping & Wu, Lan, 2013. "Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 74-85.
    25. Boonen, Tim J. & Ghossoub, Mario, 2020. "Bilateral Risk Sharing With Heterogeneous Beliefs And Exposure Constraints," ASTIN Bulletin, Cambridge University Press, vol. 50(1), pages 293-323, January.
    26. Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
    27. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    28. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    29. Rose-Anne Dana, 2002. "On Equilibria when Agents Have Multiple Priors," Annals of Operations Research, Springer, vol. 114(1), pages 105-115, August.
    30. Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2024. "Robust distortion risk measures," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 774-818, July.
    31. Paul Embrechts & Haiyan Liu & Tiantian Mao & Ruodu Wang, 2017. "Quantile-Based Risk Sharing with Heterogeneous Beliefs," Swiss Finance Institute Research Paper Series 17-65, Swiss Finance Institute, revised Jan 2018.
    32. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 189-223, August.
    33. repec:dau:papers:123456789/5456 is not listed on IDEAS
    34. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    35. repec:dau:papers:123456789/361 is not listed on IDEAS
    36. Damir Filipović & Gregor Svindland, 2008. "Optimal capital and risk allocations for law- and cash-invariant convex functions," Finance and Stochastics, Springer, vol. 12(3), pages 423-439, July.
    37. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance with belief heterogeneity," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 79-91.
    38. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292, April.
    39. repec:dau:papers:123456789/5045 is not listed on IDEAS
    40. Chan, Fung-Yee & Gerber, Hans U., 1985. "The Reinsurer's Monopoly and the Bowley Solution," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 141-148, November.
    41. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    42. Carlier, G. & Dana, R.-A., 2005. "Rearrangement inequalities in non-convex insurance models," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 483-503, August.
    43. Zhu, Michael B. & Ghossoub, Mario & Boonen, Tim J., 2023. "Equilibria and efficiency in a reinsurance market," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 24-49.
    44. repec:dau:papers:123456789/5461 is not listed on IDEAS
    45. Rose-Anne Dana, 2004. "Ambiguity, uncertainty aversion and equilibrium welfare," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 569-587, March.
    46. repec:dau:papers:123456789/5394 is not listed on IDEAS
    47. Rose‐Anne Dana, 2005. "A Representation Result For Concave Schur Concave Functions," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 613-634, October.
    48. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "Convex ordering for insurance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 409-416.
    49. Asimit, Alexandru V. & Boonen, Tim J. & Chi, Yichun & Chong, Wing Fung, 2021. "Risk sharing with multiple indemnity environments," European Journal of Operational Research, Elsevier, vol. 295(2), pages 587-603.
    50. Runhuan Feng & Chongda Liu & Stephen Taylor, 2023. "Peer-to-peer risk sharing with an application to flood risk pooling," Annals of Operations Research, Springer, vol. 321(1), pages 813-842, February.
    51. repec:dau:papers:123456789/5389 is not listed on IDEAS
    52. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    53. Boonen, Tim J. & Ghossoub, Mario, 2019. "On the existence of a representative reinsurer under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 209-225.
    54. Abdikerimova, Samal & Feng, Runhuan, 2022. "Peer-to-peer multi-risk insurance and mutual aid," European Journal of Operational Research, Elsevier, vol. 299(2), pages 735-749.
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