Skip to main content
SpringerLink
Log in

A Linear Quadratic Control for Discrete Systems with Random Parameters and Multiplicative Noise and Its Application to Investment Portfolio Optimization

  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

A quadratic control for discrete stochastic systems with random parameters and additive and multiplicative noises dependent on state and controls is studied. Equations for the optimal linear static and dynamic output controllers are derived. The controllers are robust to the type of the distribution of the vector of random parameters. The results are applied to dynamic investment portfolio optimization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Sworder, D.D., Feedback Control of a Class of Linear Systems with Jump Parameters, IEEE Trans. Autom. Control, 1969, vol. 14, no.1, pp. 9-14.

    Google Scholar 

  2. Bonhem, V.M., Stochastic Differential Equations in Control Theory, Mat. Sb. Perevodov, 1973, vol. 17, no.5, pp. 82-114.

    Google Scholar 

  3. Kazakov, I.E. and Artem'ev, V.M., Optimizatsiya dinamicheskikh sistem sluchainoi struktury (Optimization of Random-Structure Dynamic Systems), Moscow: Nauka, 1980.

    Google Scholar 

  4. Pakshin, P.V., Optimal Linear Control for Discrete Systems under Random Jump Changes of Their Parameters, Probl. Upravlen. Teor. Inf., 1982, vol. 11, no.3, pp. 179-193.

    Google Scholar 

  5. Pakshin, P.V., Stability of Discrete Random-Structure Systems under Constant Perturbations, Avtom. Telemekh., 1983, no. 6, pp. 75-85.

    Google Scholar 

  6. Hopkins, W.E., Optimal Stabilization of Families of Linear Differential Equations with Jump Coefficients and Multiplicative Noise, SIAM J. Control Optim., 1987, vol. 25, no.6, pp. 1587-1600.

    Google Scholar 

  7. Li, X., Zhou, X., and Rami, M., Indefinite Stochastic LQ Control with Jumps, Proc. 40 IEEE Conf. Decision and Control, 2001, pp. 1693-1698.

  8. De Koning, W.L., Infinite Horizon Optimal Control of Linear Discrete-Time Systems with Stochastic Parameters, Automatica, 1982, vol. 18, no.4, pp. 503-514.

    Google Scholar 

  9. Dombrovskii, V.V. and Smagin, V.I., Robust Local Optimal Tracking Control Systems, Izv. Vuzov. Fiz., 1995, no. 9, pp. 96-99.

    Google Scholar 

  10. Dombrovskii, V.V. and Chikunova, E.V., Design of Dynamic Reduced-Order Controllers for Systems with Random Parameters, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1998, no. 2, pp. 97-101.

    Google Scholar 

  11. Runolfsson, T., Risk-Sensitive and Robust Control of Discrete Time Hybrid Systems, Proc. 39 IEEE Conf. Decision and Control, 2000, pp. 1055-1060.

  12. Chen, S. and Yong, J., Stochastic Linear Quadratic Optimal Control Problems, Appl. Math. Optim., 2001, vol. 43, pp. 21-45.

    Google Scholar 

  13. Malyshev, V.V. and Pakshin, P.V., Applied Theory of Stochastic Stability and Optimal Stationary Control: A Review, Part II, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1990, no. 2, pp. 97-119.

    Google Scholar 

  14. Merton, R.C., Continuous-Time Finance, Cambridge: Blackwell, 1990.

    Google Scholar 

  15. Mel'nikov, A.V., Volkov, S.N., and Nechaev, M.L., Matematika finansovykh obyazatel'stv (Mathematics of Pecuniary Liabilities), Moscow: Vysshaya Shkola Ekonomiki, 2001.

    Google Scholar 

  16. Shepard, N., Statistical Aspects of ARCH Models and Stochastic Volatility, Obozrenie Prikl. Prom. Mat., 1996, vol. 3, pp. 764-826.

    Google Scholar 

  17. Pakshin, P.V., State Estimation and Control Design for Discrete Linear Systems with Additive and Multiplicative Noise, Avtom. Telemekh., 1978, no. 4, pp. 75-85.

    Google Scholar 

  18. Phillis, Y.A., Estimation and Control of Systems with Unknown Covariance and Multiplicative Noise, IEEE Trans. Autom. Control, 1989, vol. 34, no.10, pp. 1075-1078.

    Google Scholar 

  19. Dombrovskii, V.V., Design of Optimal Dynamic Reduced Order Controllers for Time-varying Linear Discrete Stochastic Systems, Avtom. Telemekh., 1996, no. 4, pp. 79-86.

    Google Scholar 

  20. Levine, W.S., Johnson, T.L., and Athans, M., Optimal Limited State Variable Feedback Controllers for Linear Systems, IEEE Trans. Autom. Control, 1971, vol. 16, no.6, pp. 785-793.

    Google Scholar 

  21. Dombrovsky, V.V. and Gerasimov, E.S., Dynamic Network Model of Control Investment Portfolio in Continuous Time, Proc. 5 Russian-Korean Sympos. Sci. Technol. (KORUS-2001), 2001, Tomsk, pp. 304-308.

  22. Gerasimov, E.S. and Dombrovskii, V.V., A Dynamic Network Model for Investment Control under Quadratic Risk Function, Avtom. Telemekh., 2002, no. 2, pp. 119-128.

    Google Scholar 

  23. Athans, M., The Matrix Minimum Principle, Inf. Control, 1968, vol. 11, pp. 592-606.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tomsk State University, Tomsk, Russia

    V. V. Dombrovskii & E. A. Lyashenko

Authors
  1. V. V. Dombrovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Lyashenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dombrovskii, V.V., Lyashenko, E.A. A Linear Quadratic Control for Discrete Systems with Random Parameters and Multiplicative Noise and Its Application to Investment Portfolio Optimization. Automation and Remote Control 64, 1558–1570 (2003). https://doi.org/10.1023/A:1026057305653

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026057305653

Keywords

Search

Navigation