Ograničenja u primeni direktnih i indirektnih metoda za rešavanje problema optimalne kontrole u teoriji 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 nelinearnih 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.
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