麻省理工动态最优化及其经济上的应用回归法课程全部讲义作业参考资料dynamicslides1

1、Introduction to Dynamic OptimizationNr. 1Recursive Metho dsIntroduction to Dynamic OptimizationNr. 2Outline Todays Lecture finish Euler Equations and Transversality Condition Principle of Optimality: Bellmans Equation Study of Bellman equation with bounded F contraction mapping and theorem of the ma

2、ximumIntroduction to Dynamic OptimizationNr. 3Infinite Horizon T = XV (x0) =suptF (xt, xt+1)xt+1t=0 t=0subject to,xt+1 (xt)(1)with x0 given sup tead of max definex0t+1as a plant=0 define (x0) x0t+1|x0t+1 (x0t)and x00 = x0t=0Introduction to Dynamic OptimizationNr. 4AssumptionsA1. (x) is nPon-empty fo

3、r all x XA2.limTTtF (xt, xt+1) exists for all x (x0)t=0then problem is well definedIntroduction to Dynamic OptimizationNr. 5Recursive Formulation: Bellman Equation value function satisfies () XV (x )=maxtF (x , x)0tt+1xt+1t=0t=0 xt+1(xt)X=maxF (x , x ) + maxtF (x , x)x (x )01xtt+110t+1t=1t=1xt+1(xt)

4、X=maxF (x , x ) + maxtF (x, x)x (x )01xt+1t+210t+1t=1t=0xt+1(xt)=maxF (x0, x1)+ V (x1)x1(x0)PNr. 5AIntro duction to Dynamic Optimization idea:useBE to find valueand funpctioonlicVy f unction gof OptimalityIntroduction to Dynamic OptimizationNr. 6Bellman Equation: Principle ofOptimality Principle of Optimality idea: use the functional equationV (x) =max F (x, y)+ V (y)y(x)to find V and g note: nuisance subscripts t, t + 1, dropped a solution is a function V () the same on both sides IF BE has unique so