Metrika

  • citati u SCIndeksu: 0
  • citati u CrossRef-u:[3]
  • citati u Google Scholaru:[]
  • posete u poslednjih 30 dana:11
  • preuzimanja u poslednjih 30 dana:5

Sadržaj

članak: 2 od 10  
Back povratak na rezultate
2016, vol. 44, br. 4, str. 19-46
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-adresakruna.ratkovic@gmail.com
Ključne reči: optimalna kontrola; direktne i indirektne metode; teorija rasta
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.
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
 

O članku

jezik rada: engleski
vrsta rada: izvorni naučni članak
DOI: 10.5937/industrija44-10874
objavljen u SCIndeksu: 24.02.2017.
metod recenzije: dvostruko anoniman
Creative Commons License 4.0