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Predictive control of systems with Markovian jumps under constraints and its application to the investment portfolio optimization

  • Stochastic Systems, Queueing Systems
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Abstract

In the paper, we study a problem of control with a predictive model for discrete systems with Markovian jumps and multiplicative noises. A strategy to control with regard for explicit constraints on control variables is defined. The results are applied to control an investment portfolio under constraints on investment amounts.

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References

  1. Elliott, R.J. and Van der Hoek, J., An Application of Hidden Markov Models to Asset Allocation Problems, Finance and Stochastics, 1997, no. 1, pp. 229–238.

  2. Gerasimov, E.S. and Dombrovskii, V.V., Dynamic Network Model of Managing Investment Portfolio under Random Stepwise Changes in Volatilities of Financial Assets, Autom. Remote Control, 2003, no. 7, pp. 1086–1093.

  3. Gal’perin, V.A., Dombrovskii, V.V., and Fedosov, E.N., Dynamic Control of the Investment Portfolio in the Jump-Diffusion Financial Market with Regime Switching, Autom. Remote Control, 2005, no. 5, pp. 837–850.

  4. Yin, G. and Zhou, X.Y., Markowitz Mean-Variance Portfolio Selection with Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits, IEEE Trans. Automat. Control, 2004, vol. 39, no. 3, pp. 349–360.

    Article  MathSciNet  Google Scholar 

  5. Bäuerle, N. and Rieder, U., Portfolio Optimization with Markov-Modulated Stock Prices and Interest Rates, IEEE Trans. Automat. Control, 2004, vol. 49, no. 3, pp. 442–447.

    Article  MathSciNet  Google Scholar 

  6. Costa, O.L.V. and Paulo, W.L., Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems, Eur. J. Control, 2008, no. 5, pp. 391–408.

  7. Billio, M. and Pelizzon, L., Value-at-Risk: A Multivariate Switching Regime Approach, J. Empirical Finance, 2000, no. 7, pp. 531–554.

  8. Pakshin, P.V., Diskretnye sistemy so sluchainymi parametrami i strukturoi (Discrete Systems with Random Parameters and Structure), Moscow: Fizmatlit, 1994.

    Google Scholar 

  9. Borisov, A.V., A Preliminary Analysis of Distribution of States of Special Controlled System with Random Structure, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2005, no. 1, pp. 48–62.

  10. Borisov, A.V. and Stefanovich, A.I., Optimal Filtering of States of Special Controlled Systems with Random Structure, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2007, no. 3, pp. 16–26.

  11. Pakshin, P.V. and Retinskii, D.M., Robust Stabilization of Random-Structure Systems via Switchable Static Output Feedback, Autom. Remote Control, 2005, no. 7, pp. 1153–1161.

  12. Elliott, R.J., Aggoun, L., and Moore, J.B., Hidden Markov Models: Estimation and Control, Berlin: Springer, 1995.

    MATH  Google Scholar 

  13. Dragan, V. and Morozan, T., The Linear Quadratic Optimization Problems for a Class of Linear Stochastic Systems With Multiplicative White Noise and Markovian Jumping, IEEE Trans. Automat. Control, 2004, vol. 49, no. 5, pp. 665–675.

    Article  MathSciNet  Google Scholar 

  14. Propoi, A.I., Use of Linear Programming Methods for Synthesizing Sampled-Data Automatic Systems, Autom. Remote Control, 1963, no. 7, pp. 837–844.

  15. Rawlings, J., Tutorial: Model Predictive Control Technology, Proc. Am. Control Conf., San Diego, California, 1999, pp. 662–676.

  16. Mayne, D.Q., Rawlings, J.B., Rao, C.V, and Scokaert, P.O.M., Constrained Model Predictive Control: Stability and Optimality, Automatica, 2000, vol. 36, no. 6, pp. 789–814.

    Article  MathSciNet  MATH  Google Scholar 

  17. Bemporad, A., Borrelli, F., and Morari, M., Model Predictive Control Based on Linear Programming. The Explicit Solution, IEEE Trans. Automat. Control, 2002, vol. 47, no. 12, pp. 1974–1985.

    Article  MathSciNet  Google Scholar 

  18. Bemporad, A., Morari, M., Dua, V., and Pistikopoulos, E.N., The Explicit Linear Quadratic Regulator for Constrained Systems, Automatica, 2002, vol. 38, no. 1, pp. 3–20.

    Article  MathSciNet  MATH  Google Scholar 

  19. Cuzzola, A.F., Geromel, J.C., and Morari, M., An Impoved Approach for Constrained Robust Model Predictive Control, Automatica, 2002, vol. 38, no. 7, pp. 1183–1189.

    Article  MathSciNet  MATH  Google Scholar 

  20. Seron, M.M., De Dona, J.A., and Goodwin, G.C., Global Analitical Model Predictive Control with Input Constraints, 39th IEEE Conf. Decision Control, Sydney, Australia, 12–15 December, 2000, pp. 154–159.

  21. Dombrovskii, V.V., Dombrovskii, D.V., and Lyashenko, E.A., Predictive Control of Random-parameter Systems with Multiplicative Noise. Application to Investment Portfolio Optimization, Autom. Remote Control, 2005, no. 4, pp. 583–596.

  22. Dombrovskii, V.V., Dombrovskii, D.V., and Lyashenko, E.A., Model Predictive Control of Systems with Random Dependent Parameters under Constraints and Its Application to the Investment Portfolio Optimization, Autom. Remote Control, 2006, no. 12, pp. 1927–1939.

  23. Luenberger, D.G., Investment Science, New York: Oxford Univ. Press, 1998.

    Google Scholar 

  24. Tsay, R.S., Analysis of Finansial Time Series, New York: Wiley, 2002.

    Book  Google Scholar 

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Original Russian Text © V.V. Dombrovskii, T.Yu. Ob”edko, 2011, published in Avtomatika i Telemekhanika, 2011, No. 5, pp. 96–112.

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Dombrovskii, V.V., Ob”edko, T.Y. Predictive control of systems with Markovian jumps under constraints and its application to the investment portfolio optimization. Autom Remote Control 72, 989–1003 (2011). https://doi.org/10.1134/S0005117911050079

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