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

Author

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  • 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
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    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.
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