Incremental value of information for discrete-time partially observed stochastic systems

• Autorzy: Banek T.
• Języki publikacji: EN

Abstrakty

EN

A discrete-time stochastic control problem for general (nonlinear in state, control, observation and noise) models is considered. The same noise can enter into the state and into the observation equations, and the state/observation does not need to be affine with respect to the noise. Under mild assumptions the joint distribution function of the state/observation processes is obtained and used for computing the Gateaux and Frechet derivatives of the cost function. Under partial observation the control actions are restricted by the measurability requirement and we compute the Lagrange multiplier associated with this "information constraint". The multiplier is called a "dual", or "shadow" price, and in the literature of the subject is interpreted as an incremental value of information . The present and the future are two factors appearing in the multiplier and we study how they are balanced as time goes on. An algorithm for computing extremal controls in the spirit of R. Rishel (1985) is also obtained.

Słowa kluczowe

EN

stochastic control; filtering; Hausdorff measures; change of variables formula of Federer; Lagrange multipliers; value of information

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2010
• Tom: Vol. 39, no 3
• Strony: 769--781
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Banek T.

• Department of Quantitative Methods, Faculty of Management, Technical University of Lublin, Nadbystrzycka 38, 20-618 Lublin, Poland,

Bibliografia

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• DAVIS, M.H.A., DEMPSTER, M.A.H. and ELLIOTT, R.J. (1991) On the value of information in controlled diffusion processes. Liber Amicorum for M. Zakai, Academic Press, 125-138.
• EVANS, L.C. and GARIEPY, R.F. (1992) Measure Theory and Fine Properties of Functions. CRC Press, Inc. 1992.
• FEDERER, H. (1996) Geometric Measure Theory. Springer-Verlag Berlin-Heidelberg.
• LIPTSER, R.S. and SHIRYIAEV, A.N. (1999) Statistics of Random Processes. Springer-Verlag Berlin-Heidelberg
• RISHEL, R. (1985) A nonlinear discrete time stochastic adaptive control problem, Sel. Pap. 7th. Int. Symp. Math. Theory of Networks Systems, 585-592.
• SCHWEIZER, M., BECHERER, D. and AMENDINGER, J. (2003) A monetary value for initial information in portfolio optimization. Finance and Stochastics, 7(1), 29-46.
• WETS, R.J.-B. (1975) On the relation between stochastic and deterministic optimization. In: A. Bensoussan and J.L. Lions, eds., Control Theory, Numerical Methods and Computer System Modelling. LNEMS 107, Springer-Verlag, Berlin, 350-361.
• ZABCZYK, J. (1996) Chance and Decision, Stochastic Control in Discrete Time. QUADERNI, Scuola Normale Superiore, Pisa-1996.