IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v154y2022icp1-25.html
   My bibliography  Save this article

Controlled ordinary differential equations with random path-dependent coefficients and stochastic path-dependent Hamilton–Jacobi equations

Author

Listed:
  • Qiu, Jinniao

Abstract

This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, the value function turns out to be a random field on the path space and it is characterized by a stochastic path-dependent Hamilton–Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.

Suggested Citation

  • Qiu, Jinniao, 2022. "Controlled ordinary differential equations with random path-dependent coefficients and stochastic path-dependent Hamilton–Jacobi equations," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 1-25.
    • Handle: RePEc:eee:spapps:v:154:y:2022:i:c:p:1-25
    DOI: 10.1016/j.spa.2022.09.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922001922
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.09.001?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. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    2. Detemple, Jerome B & Zapatero, Fernando, 1991. "Asset Prices in an Exchange Economy with Habit Formation," Econometrica, Econometric Society, vol. 59(6), pages 1633-1657, November.
    3. Qiu, Jinniao, 2017. "Weak solution for a class of fully nonlinear stochastic Hamilton–Jacobi–Bellman equations," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1926-1959.
    4. Christian Bender & Nikolai Dokuchaev, 2016. "A First-Order Bspde For Swing Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 461-491, 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. Christian Bayer & Jinniao Qiu & Yao Yao, 2020. "Pricing Options Under Rough Volatility with Backward SPDEs," Papers 2008.01241, arXiv.org.
    2. Francisco Gomes & Alexander Michaelides, 2003. "Portfolio Choice With Internal Habit Formation: A Life-Cycle Model With Uninsurable Labor Income Risk," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 729-766, October.
    3. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    4. Georgii Riabov & Aleh Tsyvinski, 2021. "Policy with stochastic hysteresis," Papers 2104.10225, arXiv.org.
    5. 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.
    6. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.
    7. Bandi, Federico M. & Tamoni, Andrea, 2023. "Business-cycle consumption risk and asset prices," Journal of Econometrics, Elsevier, vol. 237(2).
    8. Fan, ShengJun & Jiang, Long & Tian, DeJian, 2011. "One-dimensional BSDEs with finite and infinite time horizons," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 427-440, March.
    9. Klimsiak, Tomasz & Rzymowski, Maurycy & Słomiński, Leszek, 2019. "Reflected BSDEs with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1153-1184.
    10. Kris Jacobs, 2001. "Estimating Nonseparable Preference Specifications for Asset Market Participants," CIRANO Working Papers 2001s-12, CIRANO.
    11. Jin, Xing & Deng, Shuhui, 1997. "Existence and uniqueness of optimal consumption and portfolio rules in a continuous-time finance model with habit formation and without short sales," Journal of Mathematical Economics, Elsevier, vol. 28(2), pages 187-205, September.
    12. Weidong Tian & Murray Carlson & David A. Chapman & Ron Kaniel & Hong Yan, 2017. "Specification Error, Estimation Risk, and Conditional Portfolio Rules," International Review of Finance, International Review of Finance Ltd., vol. 17(2), pages 263-288, June.
    13. Geonwoo Kim & Junkee Jeon, 2024. "Dynamic Asset Allocation and Retirement Decision with Consumption Ratcheting and Effort Choice," Mathematics, MDPI, vol. 12(23), pages 1-18, December.
    14. Champarnaud, Luc & Michel, Philippe, 2000. "Biens culturels, transmission de culture et croissance," L'Actualité Economique, Société Canadienne de Science Economique, vol. 76(4), pages 501-520, décembre.
    15. Andrei Polbin & Sergey Drobyshevsky, 2014. "Developing a Dynamic Stochastic Model of General Equilibrium for the Russian Economy," Research Paper Series, Gaidar Institute for Economic Policy, issue 166P, pages 156-156.
    16. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    17. 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.
    18. Bowman, David & Minehart, Deborah & Rabin, Matthew, 1999. "Loss aversion in a consumption-savings model," Journal of Economic Behavior & Organization, Elsevier, vol. 38(2), pages 155-178, February.
    19. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    20. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.

    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:154:y:2022:i:c:p:1-25. 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.