IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i3p407-426.html
   My bibliography  Save this article

Ergodic BSDEs under weak dissipative assumptions

Author

Listed:
  • Debussche, Arnaud
  • Hu, Ying
  • Tessitore, Gianmario

Abstract

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in Fuhrman et al. (2009) [12]. In other words we do not need to require the uniform exponential decay of the difference of two solutions of the underlying forward equation, which, on the contrary, is assumed to be non-degenerate. We show the existence of solutions by the use of coupling estimates for a non-degenerate forward stochastic differential equation with bounded measurable nonlinearity. Moreover we prove the uniqueness of "Markovian" solutions by exploiting the recurrence of the same class of forward equations. Applications are then given for the optimal ergodic control of stochastic partial differential equations and to the associated ergodic Hamilton-Jacobi-Bellman equations.

Suggested Citation

  • Debussche, Arnaud & Hu, Ying & Tessitore, Gianmario, 2011. "Ergodic BSDEs under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 407-426, March.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:3:p:407-426
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00267-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Da Prato, Giuseppe & Debussche, Arnaud & Tubaro, Luciano, 2005. "Coupling for some partial differential equations driven by white noise," Stochastic Processes and their Applications, Elsevier, vol. 115(8), pages 1384-1407, August.
    2. Richou, Adrien, 2009. "Ergodic BSDEs and related PDEs with Neumann boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2945-2969, September.
    3. 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.
    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. Li, Juan & Zhao, Nana, 2019. "Representation of asymptotic values for nonexpansive stochastic control systems," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 634-673.
    2. Robertson, Scott & Xing, Hao, 2015. "Large time behavior of solutions to semi-linear equations with quadratic growth in the gradient," LSE Research Online Documents on Economics 60578, London School of Economics and Political Science, LSE Library.
    3. Hu, Mingshang & Wang, Falei, 2021. "Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 139-171.
    4. 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.
    5. Gechun Liang & Thaleia Zariphopoulou, 2015. "Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE," Papers 1511.04863, arXiv.org, revised Nov 2016.
    6. Bréhier, Charles-Edouard, 2012. "Strong and weak orders in averaging for SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2553-2593.
    7. Madec, P.Y., 2015. "Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1821-1860.
    8. Hu, Ying & Lemonnier, Florian, 2019. "Ergodic BSDE with unbounded and multiplicative underlying diffusion and application to large time behaviour of viscosity solution of HJB equation," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4009-4050.
    9. Wing Fung Chong & Ying Hu & Gechun Liang & Thaleia Zariphopoulou, 2019. "An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior," Finance and Stochastics, Springer, vol. 23(1), pages 239-273, January.
    10. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    11. Cosso, Andrea & Fuhrman, Marco & Pham, Huyên, 2016. "Long time asymptotics for fully nonlinear Bellman equations: A backward SDE approach," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 1932-1973.
    12. Filippo de Feo, 2020. "The Averaging Principle for Non-autonomous Slow-fast Stochastic Differential Equations and an Application to a Local Stochastic Volatility Model," Papers 2012.09082, arXiv.org, revised Jan 2021.
    13. Samuel N. Cohen & Victor Fedyashov, 2015. "Nash equilibria for non zero-sum ergodic stochastic differential games," Papers 1511.02716, arXiv.org, revised Jun 2017.

    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. Teppei Ogihara & Mitja Stadje, 2024. "Efficient drift parameter estimation for ergodic solutions of backward SDEs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1181-1205, September.
    2. Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
    3. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    4. 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.
    5. Mingyu Xu, 2007. "Reflected Backward SDEs with Two Barriers Under Monotonicity and General Increasing Conditions," Journal of Theoretical Probability, Springer, vol. 20(4), pages 1005-1039, December.
    6. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    7. 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.
    8. N'zi, Modeste & Owo, Jean-Marc, 2009. "Backward doubly stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 920-926, April.
    9. Chen, Zengjing & Kulperger, Reg, 2006. "Minimax pricing and Choquet pricing," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 518-528, June.
    10. Auguste Aman, 2012. "Reflected Generalized Backward Doubly SDEs Driven by Lévy Processes and Applications," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1153-1172, December.
    11. Bandini, Elena & Fuhrman, Marco, 2017. "Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1441-1474.
    12. Jean-François Chassagneux & Romuald Elie & Idris Kharroubi, 2015. "When terminal facelift enforces delta constraints," Finance and Stochastics, Springer, vol. 19(2), pages 329-362, April.
    13. Hyndman, Cody Blaine, 2007. "Forward-backward SDEs and the CIR model," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1676-1682, November.
    14. Leitner Johannes, 2007. "Pricing and hedging with globally and instantaneously vanishing risk," Statistics & Risk Modeling, De Gruyter, vol. 25(4), pages 311-332, October.
    15. Cao, Guilan & He, Kai, 2007. "Successive approximation of infinite dimensional semilinear backward stochastic evolution equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1251-1264, September.
    16. Reda Chhaibi & Ibrahim Ekren & Eunjung Noh & Lu Vy, 2022. "A unified approach to informed trading via Monge-Kantorovich duality," Papers 2210.17384, arXiv.org.
    17. Andrew Lesniewski & Anja Richter, 2016. "Managing counterparty credit risk via BSDEs," Papers 1608.03237, arXiv.org, revised Aug 2016.
    18. Fan, Xiliang & Ren, Yong & Zhu, Dongjin, 2010. "A note on the doubly reflected backward stochastic differential equations driven by a Lévy process," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 690-696, April.
    19. Bahlali, Khaled & Hamadène, SaI¨d & Mezerdi, Brahim, 2005. "Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1107-1129, July.
    20. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.

    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:eee:spapps:v:121:y:2011:i:3:p:407-426. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.