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Risk sharing under heterogeneous beliefs without convexity

Author

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  • Felix-Benedikt Liebrich

    (Amsterdam School of Economics)

Abstract

We consider the problem of finding (Pareto-)optimal allocations of risk among finitely many agents. The associated individual risk measures are law-invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measures. Moreover, we assume that the individual risk assessments are consistent with the respective second-order stochastic dominance relations, but remain agnostic about their convexity. A simple sufficient condition for the existence of Pareto optima is provided. The proof combines local comonotonic improvement with a Dieudonné-type argument, which also establishes a link of the optimal allocation problem to the realm of “collapse to the mean” results.

Suggested Citation

  • Felix-Benedikt Liebrich, 2024. "Risk sharing under heterogeneous beliefs without convexity," Finance and Stochastics, Springer, vol. 28(4), pages 999-1033, October.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:4:d:10.1007_s00780-024-00540-6
    DOI: 10.1007/s00780-024-00540-6
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    References listed on IDEAS

    as
    1. Chi, Yichun, 2019. "On The Optimality Of A Straight Deductible Under Belief Heterogeneity," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 243-262, January.
    2. repec:dau:papers:123456789/9713 is not listed on IDEAS
    3. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    4. Massimiliano Amarante, 2016. "A representation of risk measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 95-103, April.
    5. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    6. 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.
    7. Massoomeh Rahsepar & Foivos Xanthos, 2020. "On the extension property of dilatation monotone risk measures," Papers 2002.11865, arXiv.org.
    8. 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.
    9. 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.
    10. repec:dau:papers:123456789/5045 is not listed on IDEAS
    11. Rose-Anne Dana & Cuong Le Van, 2007. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00188761, HAL.
    12. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2018. "Law-invariant functionals on general spaces of random variables," Papers 1808.00821, arXiv.org, revised Jan 2021.
    13. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    14. Liebrich, Felix-Benedikt & Svindland, Gregor, 2019. "Efficient allocations under law-invariance: A unifying approach," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 28-45.
    15. Ludkovski, Michael & Rüschendorf, Ludger, 2008. "On comonotonicity of Pareto optimal risk sharing," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1181-1188, August.
    16. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, December.
    17. 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.
    18. Weber, Stefan, 2018. "Solvency II, or how to sweep the downside risk under the carpet," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 191-200.
    19. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    20. Liu, Haiyan, 2020. "Weighted Comonotonic Risk Sharing Under Heterogeneous Beliefs," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 647-673, May.
    21. 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.
    22. Tsanakas, Andreas, 2009. "To split or not to split: Capital allocation with convex risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 268-277, April.
    23. 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.
    24. 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.
    25. repec:dau:papers:123456789/361 is not listed on IDEAS
    26. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    27. repec:dau:papers:123456789/2342 is not listed on IDEAS
    28. 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.
    29. repec:dau:papers:123456789/342 is not listed on IDEAS
    30. Liu, Peng & Wang, Ruodu & Wei, Linxiao, 2020. "Is the inf-convolution of law-invariant preferences law-invariant?," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 144-154.
    31. Hans Föllmer & Stefan Weber, 2015. "The Axiomatic Approach to Risk Measures for Capital Determination," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 301-337, December.
    32. Tim J. Boonen, 2016. "Optimal Reinsurance with Heterogeneous Reference Probabilities," Risks, MDPI, vol. 4(3), pages 1-11, July.
    33. Mathieu Cambou & Damir Filipović, 2017. "Model Uncertainty And Scenario Aggregation," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 534-567, April.
    34. Shengzhong Chen & Niushan Gao & Foivos Xanthos, 2018. "The strong Fatou property of risk measures," Papers 1805.05259, arXiv.org.
    35. Damir Filipović & Michael Kupper, 2008. "Optimal Capital And Risk Transfers For Group Diversification," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 55-76, January.
    36. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    More about this item

    Keywords

    Risk sharing; (Pareto-)optimal allocations; Consistent risk measures; Star-shaped risk measures;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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