Geodesic
The Method of Characteristics in Macroeconomic Modeling
Contributions to game theory and management, Tome 3 (2010), pp. 399-408.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of identification of a macroeconomic model is considered for statistic data given at fixed instants in a time-interval. The model has the form of two ordinary differential equations depending of controlling parameters. A new approach is suggested to solve the identification problem in the framework of optimal control theory. A numerical algorithm based on characteristics of the Bellman equation is suggested to create and verify the model. Results of simulations are exposed.
Keywords: nonlinear system, optimal control, dynamic programming, optimal feedbacks. 
@article{CGTM_2010_3_a29,
     author = {Nina N. Subbotina and Timofei B. Tokmantsev},
     title = {The {Method} of {Characteristics} in {Macroeconomic} {Modeling}},
     journal = {Contributions to game theory and management},
     pages = {399--408},
     publisher = {mathdoc},
     volume = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2010_3_a29/}
}
TY  - JOUR
AU  - Nina N. Subbotina
AU  - Timofei B. Tokmantsev
TI  - The Method of Characteristics in Macroeconomic Modeling
JO  - Contributions to game theory and management
PY  - 2010
SP  - 399
EP  - 408
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2010_3_a29/
LA  - en
ID  - CGTM_2010_3_a29
ER  - 
%0 Journal Article
%A Nina N. Subbotina
%A Timofei B. Tokmantsev
%T The Method of Characteristics in Macroeconomic Modeling
%J Contributions to game theory and management
%D 2010
%P 399-408
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2010_3_a29/
%G en
%F CGTM_2010_3_a29
Nina N. Subbotina; Timofei B. Tokmantsev. The Method of Characteristics in Macroeconomic Modeling. Contributions to game theory and management, Tome 3 (2010), pp. 399-408. http://geodesic.mathdoc.fr/item/CGTM_2010_3_a29/

[1] Al'brekht E. G., “Methods of construction and identification of mathematical models for macroeconomic processes”, Investigated in Russia, 2002 (in Russian) http://zhurnal.ape.relarn.ru/articles/2002/005.pdf

[2] Bellman R., Dynamic programming, Princeton University Press, Princeton, NJ, 1957 | MR | Zbl

[3] Crandall M. G., Lions P.-L., “Viscosity Solutions of Hamilton–Jacobi Equations”, Trans. Am. Math. Soc., 277:1 (1983), 1–42 | DOI | MR | Zbl

[4] Krasovskii N. N., Subbotin A. I., Game-Theoretical Control Problems, Springer, New York, 1988 | MR

[5] Subbotin A. I., Generalized Solutions of First Order PDEs: The dynamical Optimization Perspectives, Birkhäuser, Boston, 1995 | MR

[6] Petrosyan L. A., “Cooperative Stochastic Games”, Adv. in Dynamic Games, Appl. Econ., Manag. Sci., Engin., and Environ. Manag., v. III, Ann. Int. Soc. Dynamic Games, 8, eds. S.. H. A. Muto, L. A. Petrosyan T. E. S. Raghavan, Birkhäuser, Boston, 2006, 139–145 | DOI | MR

[7] Subbotina N. N., “The method of characteristics for Hamilton–Jacobi equations and applications to dynamical optimization”, J. Math. Sci., 135:3 (2006), 2955–3091 | DOI | MR

[8] Subbotina N. N., Tokmantsev T. B., “A numerical method or the minimax solution of the Bellman equation in the Cauchy problem with additional restrictions”, Proc. Steklov Math. Inst., 2006, 222–229 | MR

[9] Subbotina N. N., Tokmantsev T. B., “On the effiency of optimal grid synthsis in the optiaml control problems with fixed terminal time”, Differential Equations, 45:11 (2009), 1651–1662 (in Russian) | DOI | MR | Zbl

[10] Tarasyev A. M., Watanabe C., Zhu B., “Optimal feedbacks in techno-economic dynamics”, Int. J. Technol. Managem., 23:7–8 (2002), 691–717 | DOI

[11] Zhukovskii V. I., Chikrii A. A., Lineino-kvadratichnye differentsial'nye igry, Naukova Dumka, Kiev, 1994