Abstract
For the discrete systems with random parameters perturbed by additive and multiplicative noise depending on the states and controls, design of the predictive model-based control strategies was considered. Predictive control strategies of closed-loop and open-loop types were developed. The results obtained were applied to dynamic optimization of the investment portfolio under constrained volumes of trade operations.
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REFERENCES
Rawlings, J., Tutorial: Model Predictive Control Technology, Proc. Am. Control Conf., San Diego, 1999, pp. 662–676.
Propoi, A.I., Applying the Linear Programming Methods to Design the Pulse Automatic Systems, Avtom. Telemekh., 1963, no. 7, pp. 912–920.
Chernous’ko, F.L. and Kolmanovskii, V.B., Optimal’noe upravlenie pri sluchainykh vozmushcheniyakh (Optimal Control under Random Disturbances), Moscow: Nauka, 1978.
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.
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, 2000, pp. 154–159.
Gill, P.E., Murray, W., and Wright, M.H., Practical Optimization, London: Academic, 1981. Translated under the title Prakticheskaya optimizatsiya, Moscow: Mir, 1985.
Runggaldier, W.J., On Stochastic Control in Finance, in Math. Syst. Theory in Biology, Communication, Computation and Finance, Gilliam, D. and Rosental, J., Eds., IMA Book Series (MINS-2002), New York: Springer, 2003, pp. 1–28.
Gerasimov, E.S. and Dombrovskii, V.V., Dynamic Network Model of Controlof the Investment Portfolio under Random Step Change of Volatilities of the Financial Assets, Avtom. Telemekh., 2003, no. 7, pp. 77–86.
Dombrovsky, V.V. and Lashenko, E.A., Dynamic Model of Active Portfolio Management with Stochastic Volatility in Incomplete Market, Proc. SICE Annual Conf., Fukui, Japan, 2003, pp. 636–641.
Albeverio, S. and Steblovskaya, V., A Model of Financial Market with Several Interacting Assets. Complete Market Case, Finance Stochast., 2002, no. 6, pp. 383–396.
Dombrovskii, V.V. and Lyashenko, E.A., Dynamic Model of Control of the Investment Portfolio at the Financial Market with Stochastic Volatility, Avtomat. Vychisl. Tekhn., 2003, no. 5, pp. 12–21.
Dombrovskii, V.V. and Lyashenko, E.A., Linear-quadratic Control of Discrete Random-parameter Systems with Multiplicative Noise with Application to Optimization of the Investment Portfolio, Avtom. Telemekh., 2003, no. 10, pp. 50–65.
Pakshin, P.V., Stability of Discrete Random-structure Systems under Persistent Perturbations, Avtom. Telemekh., 1983, no. 6, pp. 75–85.
Hopkins, W.E., Optimal Stabilization of Families of Linear Differential Equations with Jump Coefficients and Multiplicative Noise, SIAM J. Contr. Optimiz., 1987, vol. 25, no.6, pp. 1587–1600.
Li, X., Zhou, X., and Rami, M., Indefinite Stochastic LQ Control with Jumps, Proc. 40th IEEE Conf. Decision Control, Orlando, 2001, pp. 1693–1698.
Sharp, W.F., Alexander, G.J., and Bailey, J.V., Fundamentals of Investments, Englewood Cliffs: Prentice Hall, 1993. Translated under the title Investitsii, Moscow: INFRA-M, 1997.
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Translated from Avtomatika i Telemekhanika, No. 4, 2005, pp. 84–97.
Original Russian Text Copyright © 2005 by V. Dombrovskii, D. Dombrovskii, Lyashenko.
This paper was recommended for publication by A.I. Kibzun, a member of the Editorial Board
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Dombrovskii, V.V., Dombrovskii, D.V. & Lyashenko, E.A. Predictive control of random-parameter systems with multiplicative noise. Application to investment portfolio optimization. Autom Remote Control 66, 583–595 (2005). https://doi.org/10.1007/s10513-005-0102-5
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DOI: https://doi.org/10.1007/s10513-005-0102-5