Metrika članka

  • citati u SCindeksu: 0
  • citati u CrossRef-u:[1]
  • citati u Google Scholaru:[=>]
  • posete u poslednjih 30 dana:40
  • preuzimanja u poslednjih 30 dana:38
članak: 8 od 26  
Back povratak na rezultate
Industrija
2016, vol. 44, br. 4, str. 19-46
jezik rada: engleski
vrsta rada: izvorni naučni članak
doi:10.5937/industrija44-10874

Creative Commons License 4.0
Ograničenja u primeni direktnih i indirektnih metoda za rešavanje problema optimalne kontrole u teoriji rasta
University of Donja Gorica, Faculty of Applied Sciences, Montenegro

e-adresa: kruna.ratkovic@gmail.com

Sažetak

Fokus ovog članka je na detaljnoj i sveobuhvatnoj analizi glavnih metoda i matematičkih tehnika koje se koriste za rešavanje problema optimalne kontrole u teoriji rasta. Dat je pregled najvažnijih metoda za rešavanje dinamičkih nelineamih modela rasta koristeći optimalnu kontrolu, kao i kritički osvrt na njihova ograničenja. Osnovni problem koji treba rešiti ovim pristupom je određivanje optimalne stope rasta tokom vremena na način koji maksimizira funkciju blagostanja u beskonačnom vremenskom periodu. Funkcija blagostanja zavisi od koeficijenta kapitalne opremljenosti rada (promjenljive stanja) i od potrošnje po glavi stanovnika (kontrolne promjenljive). Numeričke metode za rešavanje problema optimalne kontrole su podeljene u dve klase: direktni i indirektni pristup. Na primjeru neoklasičnog modela rasta dat je prikaz indirektnog pristupa. Kako bi se predstavio istovremeno indirektni i direktni pristup, u radu će biti data i primena ovih metoda kod dva endogena modela: Romerov i Lucas-Uzawa model. Biće date prednosti i efikasnost jedne metode u odnosu na drugu. Iako se indirektne metode za rešavanje problema optimalne kontrole u ovoj oblasti i dalje najviše upotrebljavaju u praksi, biće viđeno da primjena direktnih metoda može biti vrlo efikasna i korisna u prevazilaženju problema koji se mogu javiti kod indirektnog pristupa.

Ključne reči

optimalna kontrola; direktne i indirektne metode; teorija rasta

Reference

Acemoglu, D. (2007) Introduction to modern economic growth (Levine's bibliography). UCLA Department of Economics
Aghion, P., Howitt, P. (1998) Endogenous growth theory. Cambridge MA: MIT
Arrow, K.J., Kurz, M. (1970) Public investment, the rate of return and optimal fiscal policy. Baltimore -, London: Johns Hopkins Press
Arrow, K.J. (1968) Applications of control theory to economic growth. Providence: American Mathematical Society, pp. 85-119
Aseev, S. (2009) Infinite-horizon optimal control with applications in growth theory: Lecture notes
Atolia, M., Chatterjee, S., Turnovsky, S.J. (2008) How Misleading is linearization?: Evaluating the dynamics of the neoclassical growth model. u: Working Papers, Florida: Department of Economics, State University
Barro, R.J., Sala-I-Martin, X. (2003) Economic growth. New York, itd: McGraw-Hill
Bellman, R.E. (1957) Dynamic programming. Princeton, NJ: Princeton University Press
Betts, J.T. (2001) Practical methods for optimal control using nonlinear programming. Philadelphia: SIAM Press
Brunner, M., Strulik, H. (2002) Solution of perfect foresight saddlepoint problems: a simple method and applications. Journal of Economic Dynamics and Control, 26(5): 737-753
Cass, D. (1965) Optimum growth in an aggregative model of capital accumulation. Review of Economic Studies, 32: 233. 240
Chiang, A.C. (1992) Elements of dynamic optimization. New York: McGraw-Hill
Dixit, A. (1990) Optimization in economic theory. Oxford, UK: Oxford University Press Inc, passim
Dorfman, R. (1969) An Economic Interpretation of Optimal Control Theory. American Economic Review, 59(5); 817-831
Fabbri, G., Gozzi, F. (2008) Solving optimal growth models with vintage capital: The dynamic programming approach. Journal of Economic Theory, 143(1): 331-373
Fontes, F.A.C.C. (2001) A general framework to design stabilizing nonlinear model predictive controllers. Systems & Control Letters, 42(2): 127-143
Gill, P.E., Murray, W., Saunders, M.A., Wong, E. (2015) User's guide for SNOPT 7. 5: Software for large-scale nonlinear programming. u: Center for Computational Mathematics Report, La Jolla, CA - San Diego: Department of Mathematics, University of California, 15-3, CCoM
Gill, P.E., Murray, W., Saunders, M.A. (2005) SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization. SIAM Review, 47(1): 99-131
Inada, K. (1963) On a Two-Sector Model of Economic Growth: Comments and a Generalization. Review of Economic Studies, 30(2): 119
Intriligator, M.D. (1971) Mathematical optimization and economic theory. Englewood Cliffs, NJ, itd: Prentice Hall
Judd, K.L. (1998) Numerical methods in economics. The MIT Press, Vol. 1
Judd, K.L. (1992) Projection methods for solving aggregate growth models. Journal of Economic Theory, 58(2): 410-452
Kamien, M.I., Schwartz, N.L. (1991) Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. Elsevier Science, 2nd ed
Koopmans, T. (1963) On the concept of optimal economic growth. u: Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University
Lopes, M.A., Fontes, F.A.C.C., Fontes, D.A.C.C. (2013) Optimal control of infinite-horizon growth models: A direct approach. u: FEP Working Papers, Universidade do Porto, Faculdade de Economia do Porto
Lucas, R.E. (1988) On the mechanics of economic development. Journal of Monetary Economics, 22, 3-42
Ljungqvist, L., Sargent, T.J. (2012) Recursive macroeconomic theory. The MIT Press, Vol. 1; 3rd ed
Mercenier, J., Michel, P. (1994) Discrete-Time Finite Horizon Approximation of Infinite Horizon Optimization Problems with Steady-State Invariance. Econometrica, 62(3): 635
Mulligan, C.B., Sala-i, M.X. (1991) A note on the time-elimination method for solving recursive dynamic economic models. u: NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc
Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F. (1964) The mathematical theory of optimal processes. New York: The Macmillan Company
Ramsey, F.P. (1928) A mathematical theory of saving. Economic Journal, vol. 38, str. 543-559
Rao, A.V. (2009) A survey of numerical methods for optimal control. Advances in the Astronautical Sciences, 135(1); 497-528
Romer, P.M. (1990) Endogenous Technological Change. Journal of Political Economy, 98(S5): S71
Romer, P.M. (1994) The origins of endogenous growth. Journal of Economic Perspectives, vol. 8, br. 1, str. 3-22
Sargent, R.W.H. (2000) Optimal control. Journal of Computational and Applied Mathematics, 124(1-2): 361-371
Solow, R.M. (1956) A contribution to the theory of economic growth. Quarterly Journal of Economics, vol. 70, br. 1, str. 65-94
Stokey, N., Lucas, R.E., Prescott, E.C. (1989) Recursive methods in economic dynamics. Cambridge, Mass: Harvard University Press
Trimborn, T., Koch, K.J., Steger, T.M. (2004) Multi-dimensional transitional dynamics: A simple numerical procedure. CER-ETH Economics working paper series
Uzawa, H. (1965) Optimum Technical Change in An Aggregative Model of Economic Growth. International Economic Review, 6(1): 18
von Stryk, O., Bulirsch, R. (1992) Direct and indirect methods for trajectory optimization. Annals of Operations Research, 37(1): 357-373
Wolman, A.L., Couper, E.A. (2003) Potential consequences of linear approximation in economics. Economic Quarterly, 51-67