Lecture Notes on Dynamic Programming Economics 200E, Professor Bergin, Spring 1998 Adapted from lecture notes of Kevin Salyer and from Stokey, Lucas and Prescott (1989) Outline 1) A Typical Problem 2) A Deterministic Finite Horizon Problem 2.1) Finding necessary conditions 2.2) A special case 2.3) Recursive solution /Rect [31.731 138.561 122.118 150.25] It provides a systematic procedure for determining the optimal com-bination of decisions. /A << /S /GoTo /D (Navigation28) >> 3 96 0 obj endobj endobj Prime. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. /Border[0 0 0]/H/N/C[.5 .5 .5] /Type /Annot << The author treats a number of topics in economics, including economic growth, macroeconomics, microeconomics, finance and dynamic games. /Border[0 0 0]/H/N/C[.5 .5 .5] << endobj /Type /Annot /Rect [31.731 231.147 91.421 240.715] /Border[0 0 0]/H/N/C[.5 .5 .5] Dynamic programming is both a mathematical optimization method and a computer programming method. >> << /Rect [31.731 57.266 352.922 68.955] 99 0 obj By applying the principle of dynamic programming the first order nec-essary conditions for this problem are given by the Hamilton-Jacobi-Bellman (HJB) equation, V(xt) = max ut {f(ut,xt)+βV(g(ut,xt))} which is usually written as V(x) = max u {f(u,x)+βV(g(u,x))} (1.1) If an optimal control u∗ exists, it has the form u∗ = h(x), where h(x) is /MediaBox [0 0 362.835 272.126] Dynamic Programming in Economics: 5: Van, Cuong, Dana, Rose-Anne: Amazon.sg: Books. 87 0 obj << xÚíXKoÜ6¾ûWè(¡Ã7)»9Ô­"¨ÑØÙ´‡¤e-Ûª½T¢ÕÚI.ýëŠzPZÉ1ì¤(Œ`±¢Dg†çEâà. /Type /Annot y˧}^õt5¼’À+ÙÒk(í¾BÜA9M‚†R`kZ‹„֢ˍNá%PçJFg:ü%¯ž\kL£÷¡P¬î½õàæ×! The Problem. << Aims: In part I (methods) we provide a rigorous introduction to dynamic problems in economics that combines the tools of dynamic programming with numerical techniques. /Type /Annot Ž•Œ}OÜÞ¼±×oß%RtÞ%>úC¿6t3AqG'#>D’fw?'Ü>. Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. Join us for Winter Bash 2020. /Border[0 0 0]/H/N/C[.5 .5 .5] /A << /S /GoTo /D (Navigation37) >> endobj Macroeconomics Lecture 6: dynamic programming methods, part four Chris Edmond 1st Semester 2019 1 /Type /Annot /Subtype /Link endobj /Rect [142.762 0.498 220.067 7.804] It gives us the tools and techniques to analyse (usually numerically but often analytically) a whole class of models in which the problems faced by economic agents have a recursive nature. /Rect [31.731 125.012 238.815 136.701] endobj 97 0 obj Behavioral Macroeconomics Via Sparse Dynamic Programming Xavier Gabaix March 16, 2017 Abstract This paper proposes a tractable way to model boundedly rational dynamic programming. /Length 1274 /Border[0 0 0]/H/N/C[.5 .5 .5] Let's review what we know so far, so that we can start thinking about how to take to the computer. 0 $\begingroup$ I try to solve the following maximization problem of a representative household with dynamic programming. /Subtype /Link /Type /Annot >> The main reference will be Stokey et al., chapters 2-4. 93 0 obj endobj The idea: Compute thesolutionsto thesubsub-problems once and store the solutions in a table, so that they can be reused (repeatedly) later. << /Subtype /Link /Annots [ 84 0 R 85 0 R 86 0 R 87 0 R 88 0 R 89 0 R 90 0 R 91 0 R 92 0 R 93 0 R 94 0 R 95 0 R 96 0 R 97 0 R 98 0 R 99 0 R ] Ask Question Asked 3 years, 5 months ago. 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