IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v159y2023icp350-390.html
   My bibliography  Save this article

Itô’s formula for flows of measures on semimartingales

Author

Listed:
  • Guo, Xin
  • Pham, Huyên
  • Wei, Xiaoli

Abstract

We establish Itô’s formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on Itô processes. Our approach is to first establish Itô’s formula for cylindrical functions and then extend it to the general case via function approximation and localization techniques.

Suggested Citation

  • Guo, Xin & Pham, Huyên & Wei, Xiaoli, 2023. "Itô’s formula for flows of measures on semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 350-390.
    • Handle: RePEc:eee:spapps:v:159:y:2023:i:c:p:350-390
    DOI: 10.1016/j.spa.2023.02.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414923000315
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2023.02.004?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. Fu, Guanxing & Horst, Ulrich, 2017. "Mean Field Games with Singular Controls," Rationality and Competition Discussion Paper Series 22, CRC TRR 190 Rationality and Competition.
    2. N. C. Framstad & B. Øksendal & A. Sulem, 2004. "Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 77-98, April.
    3. Li, Juan, 2018. "Mean-field forward and backward SDEs with jumps and associated nonlocal quasi-linear integral-PDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3118-3180.
    4. Bensoussan, A. & Frehse, J. & Yam, S.C.P., 2017. "On the interpretation of the Master Equation," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2093-2137.
    5. Medvegyev, Peter, 2007. "Stochastic Integration Theory," OUP Catalogue, Oxford University Press, number 9780199215256.
    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. Badics, Tamás, 2011. "Az arbitrázs preferenciákkal történő karakterizációjáról [On the characterization of arbitrage in terms of preferences]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(9), pages 727-742.
    2. Clémence Alasseur & Imen Ben Taher & Anis Matoussi, 2020. "An Extended Mean Field Game for Storage in Smart Grids," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 644-670, February.
    3. Valjarević, Dragana & Petrović, Ljiljana, 2012. "Statistical causality and orthogonality of local martingales," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1326-1330.
    4. Buckdahn, Rainer & Chen, Yajie & Li, Juan, 2021. "Partial derivative with respect to the measure and its application to general controlled mean-field systems," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 265-307.
    5. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2022. "A Unifying Framework for Submodular Mean Field Games," Center for Mathematical Economics Working Papers 661, Center for Mathematical Economics, Bielefeld University.
    6. Olivier Menoukeu Pamen, 2017. "Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 373-410, November.
    7. T. T. K. An & B. Øksendal, 2008. "Maximum Principle for Stochastic Differential Games with Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 463-483, December.
    8. Ren'e Aid & Matteo Basei & Giorgio Ferrari, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Papers 2305.00541, arXiv.org.
    9. Yuchao Dong & Qingxin Meng, 2019. "Second-Order Necessary Conditions for Optimal Control with Recursive Utilities," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 494-524, August.
    10. Andr'es C'ardenas & Sergio Pulido & Rafael Serrano, 2022. "Existence of optimal controls for stochastic Volterra equations," Papers 2207.05169, arXiv.org, revised Mar 2024.
    11. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Papers 2105.07213, arXiv.org.
    12. Nicolas Merener, 2012. "Swap rate variance swaps," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 249-261, May.
    13. Alain Bensoussan & Boualem Djehiche & Hamidou Tembine & Sheung Chi Phillip Yam, 2020. "Mean-Field-Type Games with Jump and Regime Switching," Dynamic Games and Applications, Springer, vol. 10(1), pages 19-57, March.
    14. Dianetti, Jodi, 2023. "Linear-Quadratic-Singular Stochastic Differential Games and Applications," Center for Mathematical Economics Working Papers 678, Center for Mathematical Economics, Bielefeld University.
    15. Davide Torre & Danilo Liuzzi & Simone Marsiglio, 2017. "Pollution Control Under Uncertainty and Sustainability Concern," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(4), pages 885-903, August.
    16. Dianetti, Jodi & Ferrari, Giorgio, 2019. "Nonzero-Sum Submodular Monotone-Follower Games. Existence and Approximation of Nash Equilibria," Center for Mathematical Economics Working Papers 605, Center for Mathematical Economics, Bielefeld University.
    17. Király, Júlia & Nagy, Márton & Szabó E., Viktor, 2008. "Egy különleges eseménysorozat elemzése - a másodrendű jelzáloghitel-piaci válság és (hazai) következményei [Analysis of a special sequence of events - the crisis on the secondary mortgage market an," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 573-621.
    18. Forster, Martin & La Torre, Davide & Lambert, Peter J., 2014. "Optimal control of inequality under uncertainty," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 53-59.
    19. Péter Farkas, 2013. "Counting Process Generated by Boundary-crossing Events. Theory and Statistical Applications," CEU Working Papers 2013_4, Department of Economics, Central European University.
    20. Takaki Hayashi & Yuta Koike, 2016. "Wavelet-based methods for high-frequency lead-lag analysis," Papers 1612.01232, arXiv.org, revised Nov 2018.

    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:159:y:2023:i:c:p:350-390. 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.