IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v136y2021icp1-56.html
   My bibliography  Save this article

Semilinear Kolmogorov equations on the space of continuous functions via BSDEs

Author

Listed:
  • Masiero, Federica
  • Orrieri, Carlo
  • Tessitore, Gianmario
  • Zanco, Giovanni

Abstract

We deal with a class of semilinear parabolic PDEs on the space of continuous functions that arise, for example, as Kolmogorov equations associated to the infinite-dimensional lifting of path-dependent SDEs. We investigate existence of smooth solutions through their representation via forward–backward stochastic systems, for which we provide the necessary regularity theory. Because of the lack of smoothing properties of the parabolic operators at hand, solutions in general will only share the same regularity as the coefficients of the equation. To conclude we exhibit an application to Hamilton–Jacobi–Bellman equations associated to suitable optimal control problems.

Suggested Citation

  • Masiero, Federica & Orrieri, Carlo & Tessitore, Gianmario & Zanco, Giovanni, 2021. "Semilinear Kolmogorov equations on the space of continuous functions via BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 1-56.
    • Handle: RePEc:eee:spapps:v:136:y:2021:i:c:p:1-56
    DOI: 10.1016/j.spa.2021.01.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414921000156
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2021.01.009?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. Guatteri, Giuseppina & Masiero, Federica & Orrieri, Carlo, 2017. "Stochastic maximum principle for SPDEs with delay," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2396-2427.
    2. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    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. Yan, Tingjin & Chiu, Mei Choi & Wong, Hoi Ying, 2023. "Portfolio liquidation with delayed information," Economic Modelling, Elsevier, vol. 126(C).
    2. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    3. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," Working Papers halshs-01982243, HAL.
    4. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    5. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    6. Georgii Riabov & Aleh Tsyvinski, 2021. "Policy with stochastic hysteresis," Papers 2104.10225, arXiv.org.
    7. Briand, Philippe & Cardaliaguet, Pierre & Chaudru de Raynal, Paul-Éric & Hu, Ying, 2020. "Forward and backward stochastic differential equations with normal constraints in law," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7021-7097.
    8. Giorgio Fabbri & Francesco Russo, 2017. "HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition," LIDAM Discussion Papers IRES 2017003, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    9. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    10. Michele Giordano & Anton Yurchenko-Tytarenko, 2024. "Optimal control in linear-quadratic stochastic advertising models with memory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 275-298, June.
    11. Paulwin Graewe & Ulrich Horst & Eric S'er'e, 2013. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Papers 1309.0474, arXiv.org, revised Jun 2017.
    12. Bambi, Mauro & Gozzi, Fausto, 2020. "Internal habits formation and optimality," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 165-172.
    13. Hidekazu Yoshioka & Yuta Yaegashi, 2020. "A growth rate control problem of harmful species population and its application to algae bloom," Environment Systems and Decisions, Springer, vol. 40(1), pages 107-124, March.
    14. Ulrich Horst & Xiaonyu Xia, 2018. "Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint," Papers 1809.01972, arXiv.org, revised Apr 2020.
    15. Bruno Bouchard & Boualem Djehiche & Idris Kharroubi, 2020. "Quenched Mass Transport of Particles Toward a Target," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 345-374, August.
    16. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "A dynamic theory of spatial externalities," Working Papers halshs-02613177, HAL.
    17. Robert Balkin & Hector D. Ceniceros & Ruimeng Hu, 2023. "Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms," Papers 2307.06450, arXiv.org.
    18. Alexander M. G. Cox & Sigrid Kallblad & Martin Larsson & Sara Svaluto-Ferro, 2021. "Controlled Measure-Valued Martingales: a Viscosity Solution Approach," Papers 2109.00064, arXiv.org, revised Aug 2023.
    19. Hanchao Liu & Dena Firoozi, 2024. "Hilbert Space-Valued LQ Mean Field Games: An Infinite-Dimensional Analysis," Papers 2403.01012, arXiv.org, revised Jul 2024.
    20. Djehiche, Boualem & Gozzi, Fausto & Zanco, Giovanni & Zanella, Margherita, 2022. "Optimal portfolio choice with path dependent benchmarked labor income: A mean field model," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 48-85.

    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:136:y:2021:i:c:p:1-56. 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.