IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1410.6144.html
   My bibliography  Save this paper

Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model

Author

Listed:
  • Dmitry Kramkov
  • Sergio Pulido

Abstract

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and derive their analytic expansions for small risk aversion coefficients of the dealer.

Suggested Citation

  • Dmitry Kramkov & Sergio Pulido, 2014. "Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model," Papers 1410.6144, arXiv.org, revised Aug 2016.
    • Handle: RePEc:arx:papers:1410.6144
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1410.6144
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dmitry Kramkov & Sergio Pulido, 2014. "A system of quadratic BSDEs arising in a price impact model," Papers 1408.0916, arXiv.org, revised May 2016.
    2. repec:bla:jfinan:v:43:y:1988:i:3:p:617-37 is not listed on IDEAS
    3. Grossman, S.J. & Miller, M.H., 1988. "Liquidity And Market Structure," Papers 88, Princeton, Department of Economics - Financial Research Center.
    4. Briand, Philippe & Elie, Romuald, 2013. "A simple constructive approach to quadratic BSDEs with or without delay," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2921-2939.
    5. Nicolae Garleanu & Lasse Heje Pedersen & Allen M. Poteshman, 2009. "Demand-Based Option Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 22(10), pages 4259-4299, October.
    6. Frei, Christoph, 2014. "Splitting multidimensional BSDEs and finding local equilibria," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2654-2671.
    7. 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.
    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. Ying Hu & Gechun Liang & Shanjian Tang, 2018. "Systems of ergodic BSDEs arising in regime switching forward performance processes," Papers 1807.01816, arXiv.org, revised Jun 2020.
    2. Peter Bank & Ibrahim Ekren & Johannes Muhle-Karbe, 2018. "Liquidity in Competitive Dealer Markets," Papers 1807.08278, arXiv.org, revised Mar 2021.
    3. Peter Bank & Ibrahim Ekren & Johannes Muhle‐Karbe, 2021. "Liquidity in competitive dealer markets," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 827-856, July.
    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. 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.

    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. Dmitry Kramkov & Sergio Pulido, 2016. "Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model," Post-Print hal-01181147, HAL.
    2. Dmitry Kramkov & Sergio Pulido, 2016. "Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model," Working Papers hal-01181147, HAL.
    3. repec:hal:wpaper:hal-01147411 is not listed on IDEAS
    4. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
    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. 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.
    7. Dmitry Kramkov & Sergio Pulido, 2016. "A system of quadratic BSDEs arising in a price impact model," Post-Print hal-01147411, HAL.
    8. Constantinos Kardaras & Hao Xing & Gordan v{Z}itkovi'c, 2015. "Incomplete stochastic equilibria for dynamic monetary utility," Papers 1505.07224, arXiv.org, revised Feb 2017.
    9. 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.
    10. Jana Bielagk & Arnaud Lionnet & Goncalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Papers 1511.04218, arXiv.org, revised Feb 2017.
    11. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.
    12. Ying Hu & Gechun Liang & Shanjian Tang, 2018. "Systems of ergodic BSDEs arising in regime switching forward performance processes," Papers 1807.01816, arXiv.org, revised Jun 2020.
    13. Martin Herdegen & Johannes Muhle-Karbe & Dylan Possamai, 2019. "Equilibrium Asset Pricing with Transaction Costs," Papers 1901.10989, arXiv.org, revised Sep 2020.
    14. 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.
    15. Peter Bank & Ibrahim Ekren & Johannes Muhle-Karbe, 2018. "Liquidity in Competitive Dealer Markets," Papers 1807.08278, arXiv.org, revised Mar 2021.
    16. 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.
    17. 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.
    18. 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.
    19. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, December.
    20. Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
    21. Jackson, Joe & Žitković, Gordan, 2022. "A characterization of solutions of quadratic BSDEs and a new approach to existence," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 210-225.

    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:1410.6144. 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.