IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2008.03500.html
   My bibliography  Save this paper

Radner equilibrium and systems of quadratic BSDEs with discontinuous generators

Author

Listed:
  • Luis Escauriaza
  • Daniel C. Schwarz
  • Hao Xing

Abstract

Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in $Z$. Using unique continuation and backward uniqueness, we show that the set of discontinuity has measure zero. In a continuous-time stochastic model of an endowment economy, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility.

Suggested Citation

  • Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.
  • Handle: RePEc:arx:papers:2008.03500
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2008.03500
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    2. Peter O. Christensen & Kasper Larsen, 2014. "Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 4(2), pages 247-285.
    3. Christensen, Peter Ove & Larsen, Kasper & Munk, Claus, 2012. "Equilibrium in securities markets with heterogeneous investors and unspanned income risk," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1035-1063.
    4. Riedel, Frank & Herzberg, Frederik, 2013. "Existence of financial equilibria in continuous time with potentially complete markets," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 398-404.
    5. Dmitry Kramkov & Sergio Pulido, 2014. "A system of quadratic BSDEs arising in a price impact model," Papers 1408.0916, arXiv.org, revised May 2016.
    6. Daniel C. Schwarz, 2017. "Market completion with derivative securities," Finance and Stochastics, Springer, vol. 21(1), pages 263-284, January.
    7. Robert M. Anderson & Roberto C. Raimondo, 2008. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Econometrica, Econometric Society, vol. 76(4), pages 841-907, July.
    8. Dmitry Kramkov, 2015. "Existence of an endogenously complete equilibrium driven by a diffusion," Finance and Stochastics, Springer, vol. 19(1), pages 1-22, January.
    9. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    10. Dmitry Kramkov & Sergio Pulido, 2016. "A system of quadratic BSDEs arising in a price impact model," Post-Print hal-01147411, HAL.
    11. Hu, Ying & Tang, Shanjian, 2016. "Multi-dimensional backward stochastic differential equations of diagonally quadratic generators," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1066-1086.
    12. Kim Weston & Gordan Žitković, 2020. "An incomplete equilibrium with a stochastic annuity," Finance and Stochastics, Springer, vol. 24(2), pages 359-382, April.
    13. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    14. J. Hugonnier & S. Malamud & E. Trubowitz, 2012. "Endogenous Completeness of Diffusion Driven Equilibrium Markets," Econometrica, Econometric Society, vol. 80(3), pages 1249-1270, May.
    15. Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.
    16. Gordan Žitković, 2012. "An example of a stochastic equilibrium with incomplete markets," Finance and Stochastics, Springer, vol. 16(2), pages 177-206, April.
    17. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
    18. Jin Choi & Kasper Larsen, 2015. "Taylor approximation of incomplete Radner equilibrium models," Finance and Stochastics, Springer, vol. 19(3), pages 653-679, July.
    Full references (including those not matched with items on IDEAS)

    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. Kim Weston, 2022. "Existence of an equilibrium with limited participation," Papers 2206.12399, arXiv.org.
    2. Dmitry Kramkov & Sergio Pulido, 2017. "Density of the set of probability measures with the martingale representation property," Working Papers hal-01598651, HAL.
    3. Kasper Larsen & Tanawit Sae Sue, 2015. "Radner equilibrium in incomplete Levy models," Papers 1507.02974, arXiv.org, revised Jul 2015.
    4. Hernández, Camilo, 2023. "On quadratic multidimensional type-I BSVIEs, infinite families of BSDEs and their applications," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 249-298.
    5. Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.
    6. Dmitry Kramkov & Sergio Pulido, 2019. "Density of the set of probability measures with the martingale representation property," Post-Print hal-01598651, HAL.
    7. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," CARF F-Series CARF-F-509, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.
    9. Martin Herdegen & Johannes Muhle-Karbe & Dylan Possamaï, 2021. "Equilibrium asset pricing with transaction costs," Finance and Stochastics, Springer, vol. 25(2), pages 231-275, April.
    10. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2016. "Existence and uniqueness results for BSDEs with jumps: the whole nine yards," Papers 1607.04214, arXiv.org, revised Nov 2018.
    11. Masaaki Fujii & Akihiko Takahashi, 2021. "``Equilibrium Price Formation with a Major Player and its Mean Field Limit''," CIRJE F-Series CIRJE-F-1162, CIRJE, Faculty of Economics, University of Tokyo.
    12. Dmitry Kramkov & Sergio Pulido, 2017. "Density of the set of probability measures with the martingale representation property," Papers 1709.07329, arXiv.org, revised Jul 2019.
    13. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CARF F-Series CARF-F-495, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    14. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CIRJE F-Series CIRJE-F-1156, CIRJE, Faculty of Economics, University of Tokyo.
    15. Masaaki Fujii & Akihiko Takahashi, 2020. "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium," Papers 2010.09186, arXiv.org, revised Dec 2021.
    16. Kim Weston & Gordan Žitković, 2020. "An incomplete equilibrium with a stochastic annuity," Finance and Stochastics, Springer, vol. 24(2), pages 359-382, April.
    17. Nam, Kihun, 2021. "Locally Lipschitz BSDE driven by a continuous martingale a path-derivative approach," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 376-411.
    18. Patrick Beissner & Frank Riedel, 2018. "Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty," Finance and Stochastics, Springer, vol. 22(3), pages 603-620, July.
    19. Kizaki, Keisuke & Saito, Taiga & Takahashi, Akihiko, 2024. "A multi-agent incomplete equilibrium model and its applications to reinsurance pricing and life-cycle investment," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 132-155.
    20. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.

    More about this item

    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:arx:papers:2008.03500. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.