IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v512y2018icp507-522.html
   My bibliography  Save this article

Optimal control design for a class of quantum stochastic systems with financial applications

Author

Listed:
  • Yaghobipour, S.
  • Yarahmadi, M.

Abstract

The purpose of this paper is to design an optimal quantum controller for a class of stochastic systems with application in financial problems. Dynamics of the system is prescribed via a Quantum Stochastic Differential System (QSDES) with a quantum Brownian motion on a quantum probability space. A theorem for guaranteeing the existence and uniqueness of solutions to the QSDES is proved. Additionally, a new optimal stochastic control problem is formulated and based on the necessary optimality conditions, an optimal quantum control law is designed, explicitly. Four theorems and two lemmas, for facilitating the optimal controller design algorithm, are proved. Finally, for demonstrating the applicable results, two financial problems, Merton portfolio allocation and optimal pairs trading problem are simulated by using the presented method. As the simulation results indicate, portfolio optimal performances, minimum risk and maximum return, are achieved via presented method.

Suggested Citation

  • Yaghobipour, S. & Yarahmadi, M., 2018. "Optimal control design for a class of quantum stochastic systems with financial applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 507-522.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:507-522
    DOI: 10.1016/j.physa.2018.08.141
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118310197
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.08.141?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. Liviu-Adrian Cotfas, 2012. "Finite quantum mechanical model for the stock market," Papers 1208.6146, arXiv.org, revised Sep 2012.
    2. Zhang, Chao & Huang, Lu, 2010. "A quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5769-5775.
    3. Liviu-Adrian Cotfas, 2012. "A finite-dimensional quantum model for the stock market," Papers 1204.4614, arXiv.org, revised Sep 2012.
    4. 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.
    5. Chao Zhang & Lu Huang, 2010. "A quantum model for the stock market," Papers 1009.4843, arXiv.org, revised Oct 2010.
    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. Khaje khabaz, Moahamad & Eftekhari, S. Ali & Hashemian, Mohamad & Toghraie, Davood, 2020. "Optimal vibration control of multi-layer micro-beams actuated by piezoelectric layer based on modified couple stress and surface stress elasticity theories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 546(C).

    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. Godinho, Cresus F.L. & Abreu, Everton M.C., 2021. "The analysis of the dynamic optimization problem in econophysics from the point of view of the symplectic approach for constrained systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.
    3. Bikramaditya Ghosh & Krishna MC, 2020. "Econophysical bourse volatility – Global Evidence," Journal of Central Banking Theory and Practice, Central bank of Montenegro, vol. 9(2), pages 87-107.
    4. Pedram, Pouria, 2012. "The minimal length uncertainty and the quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2100-2105.
    5. Liviu-Adrian Cotfas, 2012. "Finite quantum mechanical model for the stock market," Papers 1208.6146, arXiv.org, revised Sep 2012.
    6. Jasmina Jekni'c-Dugi'c & Sonja Radi' c & Igor Petrovi'c & Momir Arsenijevi'c & Miroljub Dugi'c, 2018. "Quantum Brownian oscillator for the stock market," Papers 1901.10544, arXiv.org.
    7. Meng, Xiangyi & Zhang, Jian-Wei & Guo, Hong, 2016. "Quantum Brownian motion model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 281-288.
    8. Pouria Pedram, 2011. "The minimal length uncertainty and the quantum model for the stock market," Papers 1111.6859, arXiv.org, revised Jan 2012.
    9. Cotfas, Liviu-Adrian, 2013. "A finite-dimensional quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 371-380.
    10. Meng, Xiangyi & Zhang, Jian-Wei & Xu, Jingjing & Guo, Hong, 2015. "Quantum spatial-periodic harmonic model for daily price-limited stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 154-160.
    11. Gao, Tingting & Chen, Yu, 2017. "A quantum anharmonic oscillator model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 307-314.
    12. Liviu-Adrian Cotfas, 2012. "A finite-dimensional quantum model for the stock market," Papers 1204.4614, arXiv.org, revised Sep 2012.
    13. Jack Sarkissian, 2016. "Quantum theory of securities price formation in financial markets," Papers 1605.04948, arXiv.org, revised May 2016.
    14. Jack Sarkissian, 2016. "Spread, volatility, and volume relationship in financial markets and market making profit optimization," Papers 1606.07381, arXiv.org.
    15. Kumar, Sushil & Kumar, Sunil & Kumar, Pawan, 2020. "Diffusion entropy analysis and random matrix analysis of the Indian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    16. Xiangyi Meng & Jian-Wei Zhang & Jingjing Xu & Hong Guo, 2014. "Quantum spatial-periodic harmonic model for daily price-limited stock markets," Papers 1405.4490, arXiv.org.
    17. Kuzu, Erkan & Süsay, Aynur & Tanrıöven, Cihan, 2022. "A model study for calculation of the temperatures of major stock markets in the world with the quantum simulation and determination of the crisis periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    18. Pineiro-Chousa, Juan & Vizcaíno-González, Marcos, 2016. "A quantum derivation of a reputational risk premium," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 304-309.
    19. 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.
    20. 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.

    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:phsmap:v:512:y:2018:i:c:p:507-522. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.