IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1604.06609.html
   My bibliography  Save this paper

Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications

Author

Listed:
  • Huy^en Pham

    (LPMA, CREST)

Abstract

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are introduced, and following the dynamic programming approach in [32], we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations. We present several financial applications with explicit solutions, and revisit in particular optimal tracking problems with price impact, and the conditional mean-variance portfolio selection in incomplete market model.

Suggested Citation

  • Huy^en Pham, 2016. "Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications ," Papers 1604.06609, arXiv.org, revised Mar 2017.
    • Handle: RePEc:arx:papers:1604.06609
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1604.06609
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    2. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    3. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    4. Christoph Frei & Nicholas Westray, 2015. "Optimal Execution Of A Vwap Order: A Stochastic Control Approach," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 612-639, July.
    5. Jiatu Cai & Mathieu Rosenbaum & Peter Tankov, 2015. "Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach," Papers 1510.04295, arXiv.org.
    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. Huyên Pham, 2017. "Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications ," Working Papers hal-01305929, HAL.
    2. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    3. Peter Bank & Mete Soner & Moritz Vo{ss}, 2015. "Hedging with Temporary Price Impact," Papers 1510.03223, arXiv.org, revised Jul 2016.
    4. Daniel Hern'andez-Hern'andez & Harold A. Moreno-Franco & Jos'e Luis P'erez, 2017. "Periodic strategies in optimal execution with multiplicative price impact," Papers 1705.00284, arXiv.org, revised May 2018.
    5. Xiaoyue Li & John M. Mulvey, 2023. "Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network," Papers 2306.08809, arXiv.org.
    6. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    7. Panayi, Efstathios & Peters, Gareth W. & Danielsson, Jon & Zigrand, Jean-Pierre, 2018. "Designating market maker behaviour in limit order book markets," Econometrics and Statistics, Elsevier, vol. 5(C), pages 20-44.
    8. Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
    9. Ulrich Horst & Michael Paulsen, 2017. "A Law of Large Numbers for Limit Order Books," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1280-1312, November.
    10. Yamamoto, Ryuichi, 2019. "Dynamic Predictor Selection And Order Splitting In A Limit Order Market," Macroeconomic Dynamics, Cambridge University Press, vol. 23(5), pages 1757-1792, July.
    11. Aur'elien Alfonsi & Alexander Schied & Florian Klock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised Sep 2015.
    12. Alberto Ciacci & Takumi Sueshige & Hideki Takayasu & Kim Christensen & Misako Takayasu, 2020. "The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    13. Marcel Nutz & Kevin Webster & Long Zhao, 2023. "Unwinding Stochastic Order Flow: When to Warehouse Trades," Papers 2310.14144, arXiv.org.
    14. Gerry Tsoukalas & Jiang Wang & Kay Giesecke, 2019. "Dynamic Portfolio Execution," Management Science, INFORMS, vol. 67(5), pages 2015-2040, May.
    15. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    16. Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag`es, 2011. "Optimal posting price of limit orders: learning by trading," Papers 1112.2397, arXiv.org, revised Sep 2012.
    17. Rene Carmona & Kevin Webster, 2019. "Applications of a New Self-Financing Equation," Papers 1905.04137, arXiv.org.
    18. Hai-Chuan Xu & Wei Chen & Xiong Xiong & Wei Zhang & Wei-Xing Zhou & H Eugene Stanley, 2016. "Limit-order book resiliency after effective market orders: Spread, depth and intensity," Papers 1602.00731, arXiv.org, revised Feb 2017.
    19. Peter Bank & Antje Fruth, 2013. "Optimal Order Scheduling for Deterministic Liquidity Patterns," Papers 1310.3077, arXiv.org.
    20. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1604.06609. 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.