Abstract
In this paper we describe the algorithm OPTCON which has been developed for the optimal control of nonlinear stochastic models. It can be applied to obtain approximate numerical solutions of control problems where the objective function is quadratic and the dynamic system is nonlinear. In addition to the usual additive uncertainty, some or all of the parameters of the model may be stochastic variables. The optimal values of the control variables are computed in an iterative fashion: First, the time-invariant nonlinear system is linearized around a reference path and approximated by a time-varying linear system. Second, this new problem is solved by applying Bellman's principle of optimality. The resulting feedback equations are used to project expected optimal state and control variables. These projections then serve as a new reference path, and the two steps are repeated until convergence is reached. The algorithm has been implemented in the statistical programming system GAUSS. We derive some mathematical results needed for the algorithm and give an overview of the structure of OPTCON. Moreover, we report on some tentative applications of OPTCON to two small macroeconometric models for Austria.
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References
M. Aoki,Optimal Control and System Theory in Dynamic Economic Analysis (North-Holland, New York, 1976).
G.C. Chow,Analysis and Control of Dynamic Economic Systems (Wiley, New York, 1975).
G.C. Chow,Econometric Analysis by Control Methods (Wiley, New York, 1981).
P. Coomes, PLEM: A computer program — passive learning stochastic control for reduced-form econometric models, Discussion paper 85-4, Center for Economic Research, University of Texas, Austin (1985).
D.A. Kendrick,Stochastic Control for Economic Models (McGraw-Hill, New York, 1981).
D.A. Kendrick,Feedback: A New Framework for Macroeconomic Policy (Kluwer, Dordrecht, 1988).
D.A. Kendrick and P. Coomes, DUAL, A program for quadratic-linear stochastic control problems, Discussion paper 84-15, Center for Economic Research, University of Texas, Austin (1984).
E.C. MacRae, Matrix derivatives with an application to an adaptive linear decision problem, Ann. Statist. 2(1974)337.
E.C. MacRae, An adaptive learning rule for multiperiod decision problems, Econometrica 43(1975)893.
J. Matulka and R. Neck, Optimal control of nonlinear stochastic macroeconometric models: An algorithm and an economic example, in:Econometric Decision Models: New Methods of Modeling and Applications, ed. J. Gruber (Berlin, 1991) p. 57.
R. Neck, Stochastic control theory and its applications to models of operations research and economics, in:Symulacyjne Modele Przedsiebiorstw, ed. L. Piecuch (Cracow, 1989) p. 137.
R. Neck and J. Matulka, Stochastic optimum control of macroeconometric models using the algorithm OPTCON, Working Paper, Vienna University of Economics and Business Administration, Vienna, Austria (1991).
A.L. Norman, First order dual control, Ann. Econ. Social Measurement 5(1976)311.
C.S. Tapiero,Applied Stochastic Models and Control in Management (North-Holland, Amsterdam, 1988).
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Matulka, J., Neck, R. Opticon: An algorithm for the optimal control of nonlinear stochastic models. Ann Oper Res 37, 375–401 (1992). https://doi.org/10.1007/BF02071066
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DOI: https://doi.org/10.1007/BF02071066