IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v21y2017i3d10.1007_s00780-017-0323-9.html
   My bibliography  Save this article

Equilibrium in risk-sharing games

Author

Listed:
  • Michail Anthropelos

    (University of Piraeus)

  • Constantinos Kardaras

    (London School of Economics and Political Science)

Abstract

The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. In this paper, we propose a game where agents’ strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow–Debreu sharing rules. First, it is shown that agents’ best response problems have unique solutions. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation, and it is proved to exist for an arbitrary number of agents and to be unique in the two-agent game. In equilibrium, agents declare beliefs on future random outcomes different from their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (among other things) loss of efficiency. In addition, an analysis regarding extremely risk-tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium than compared to the Arrow–Debreu one.

Suggested Citation

  • Michail Anthropelos & Constantinos Kardaras, 2017. "Equilibrium in risk-sharing games," Finance and Stochastics, Springer, vol. 21(3), pages 815-865, July.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:3:d:10.1007_s00780-017-0323-9
    DOI: 10.1007/s00780-017-0323-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-017-0323-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-017-0323-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luis Braido, 2005. "General equilibrium with endogenous securities and moral hazard," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 85-101, July.
    2. Rohit Rahi & Jean-Pierre Zigrand, 2009. "Strategic Financial Innovation in Segmented Markets," The Review of Financial Studies, Society for Financial Studies, vol. 22(8), pages 2941-2971, August.
    3. Viral V. Acharya & Alberto Bisin, 2005. "Optimal Financial-Market Integration and Security Design," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2397-2434, November.
    4. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    5. Allen, Franklin & Gale, Douglas, 1991. "Arbitrage, Short Sales, and Financial Innovation," Econometrica, Econometric Society, vol. 59(4), pages 1041-1068, July.
    6. Ulf Axelson, 2007. "Security Design with Investor Private Information," Journal of Finance, American Finance Association, vol. 62(6), pages 2587-2632, December.
    7. Bisin, Alberto, 1998. "General Equilibrium with Endogenously Incomplete Financial Markets," Journal of Economic Theory, Elsevier, vol. 82(1), pages 19-45, September.
    8. John D. Finnerty, 1992. "An Overview Of Corporate Securities Innovation," Journal of Applied Corporate Finance, Morgan Stanley, vol. 4(4), pages 23-39, January.
    9. In-Uck Park, 2004. "Moral Hazard Contracting and Private Credit Markets," Econometrica, Econometric Society, vol. 72(3), pages 701-746, May.
    10. 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.
    11. Albert S. Kyle, 1989. "Informed Speculation with Imperfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 317-355.
    12. Bühlmann, Hans & Jewell, William S., 1979. "Optimal Risk Exchanges," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 243-262, December.
    13. Marzena Rostek & Marek Weretka, 2015. "Dynamic Thin Markets," The Review of Financial Studies, Society for Financial Studies, vol. 28(10), pages 2946-2992.
    14. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April.
    15. 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.
    16. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    17. Andrés Carvajal & Marzena Rostek & Marek Weretka, 2012. "Competition in Financial Innovation," Econometrica, Econometric Society, vol. 80(5), pages 1895-1936, September.
    18. Dimitri Vayanos, 1999. "Strategic Trading and Welfare in a Dynamic Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 219-254.
    19. José M. Marín & Rohit Rahi, 2000. "Information Revelation and Market Incompleteness," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 563-579.
    20. Varian, Hal R, 1985. "Divergence of Opinion in Complete Markets: A Note," Journal of Finance, American Finance Association, vol. 40(1), pages 309-317, March.
    21. repec:dau:papers:123456789/361 is not listed on IDEAS
    22. 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.
    23. 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.
    24. Nachman, David C & Noe, Thomas H, 1994. "Optimal Design of Securities under Asymmetric Information," The Review of Financial Studies, Society for Financial Studies, vol. 7(1), pages 1-44.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michail Anthropelos & Constantinos Kardaras & Georgios Vichos, 2020. "Effective risk aversion in thin risk‐sharing markets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1565-1590, October.
    2. Koster, Maurice & Boonen, Tim J., 2019. "Constrained stochastic cost allocation," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 20-30.
    3. Anthropelos, Michail & Boonen, Tim J., 2020. "Nash equilibria in optimal reinsurance bargaining," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 196-205.
    4. 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.
    5. Wang, Ruodu & Wei, Yunran, 2020. "Characterizing optimal allocations in quantile-based risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 288-300.
    6. Maxim Bichuch & Zachary Feinstein, 2020. "Endogenous inverse demand functions," Papers 2012.08002, arXiv.org, revised Apr 2022.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michail Anthropelos & Constantinos Kardaras, 2014. "Equilibrium in risk-sharing games," Papers 1412.4208, arXiv.org, revised Jul 2016.
    2. Alessandro Doldi & Marco Frittelli, 2019. "Multivariate Systemic Optimal Risk Transfer Equilibrium," Papers 1912.12226, arXiv.org, revised Oct 2021.
    3. 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 1-31, December.
    4. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2017. "The composite iteration algorithm for finding efficient and financially fair risk-sharing rules," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 122-133.
    5. Francesca Biagini & Alessandro Doldi & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2019. "Systemic Optimal Risk Transfer Equilibrium," Papers 1907.04257, arXiv.org, revised Jun 2020.
    6. Kiesel, Swen & Rüschendorf, Ludger, 2010. "On optimal allocation of risk vectors," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 167-175, October.
    7. Michail Anthropelos & Constantinos Kardaras & Georgios Vichos, 2020. "Effective risk aversion in thin risk‐sharing markets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1565-1590, October.
    8. Babus, Ana & Hachem, Kinda, 2023. "Markets for financial innovation," Journal of Economic Theory, Elsevier, vol. 208(C).
    9. Rose-Anne Dana & Cuong Le Van, 2008. "No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity," Documents de travail du Centre d'Economie de la Sorbonne b08039, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.
    10. Dana, R.A. & Le Van, C., 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2186-2202, November.
    11. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2018. "Optimal Investment, Demand and Arbitrage under Price Impact," Papers 1804.09151, arXiv.org, revised Dec 2018.
    12. Mitja Stadje, 2018. "Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk Sharing," Papers 1811.09615, arXiv.org, revised Dec 2018.
    13. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    14. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2020. "Inf-convolution and optimal risk sharing with countable sets of risk measures," Papers 2003.05797, arXiv.org, revised Mar 2022.
    15. Wang, Ruodu & Wei, Yunran, 2020. "Characterizing optimal allocations in quantile-based risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 288-300.
    16. Andreas Haier & Ilya Molchanov & Michael Schmutz, 2015. "Intragroup transfers, intragroup diversification and their risk assessment," Papers 1511.06320, arXiv.org, revised Nov 2016.
    17. Svindland Gregor, 2009. "Subgradients of law-invariant convex risk measures on L," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 169-199, December.
    18. Felix-Benedikt Liebrich, 2021. "Risk sharing under heterogeneous beliefs without convexity," Papers 2108.05791, arXiv.org, revised May 2022.
    19. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    20. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," LSE Research Online Documents on Economics 50119, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

    Nash equilibrium; Risk sharing; Heterogeneous beliefs; Reporting of beliefs;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:21:y:2017:i:3:d:10.1007_s00780-017-0323-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.