>> Dynamic Programming with Expectations II G(x,z) is a set-valued mapping or a correspondence: G : X Z X. z (t) follows a (ârst-order) Markov chain: current value of z (t) only depends on its last period value, z (t 1): Pr[z (t) = z j j z (0),...,z (t 1)] Pr[z (t) = z j j z (t 1)]. /Subtype /Link Let's review what we know so far, so that we can ⦠In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive ⦠<< Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. We want to find a sequence \(\{x_t\}_{t=0}^\infty\) and a function \(V^*:X\to\mathbb{R}\) such that << /Border[0 0 0]/H/N/C[.5 .5 .5] 86 0 obj << & O.C. Swag is coming back! Macroeconomists use dynamic programming in three different ways, illustrated in these problems and in the Macro-Lab example. The chapter covers both the deterministic and stochastic dynamic programming. /Rect [142.762 0.498 220.067 7.804] It can be used by students and researchers in Mathematics as well as in Economics. << /Subtype /Link /Rect [31.731 154.231 147.94 163.8] /Contents 102 0 R endobj /Rect [19.61 34.547 64.527 46.236] Remark: We trade space for time. /A << /S /GoTo /D (Navigation24) >> We have studied the theory of dynamic programming in discrete time under certainty. 93 0 obj >> Either formulated as a social plannerâs problem or formulated as an equilibrium problem, with each agent maximiz- However, my last result is not similar to the solution. /Font << /F21 81 0 R /F16 80 0 R /F38 105 0 R /F26 106 0 R >> /Border[0 0 0]/H/N/C[.5 .5 .5] We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. Program in Economics, HUST Changsheng Xu, Shihui Ma, Ming Yi (yiming@hust.edu.cn) School of Economics, Huazhong University of Science and Technology This version: November 29, 2018 Ming Yi (Econ@HUST) Doctoral Macroeconomics Notes on D.P. In contrast to linear programming, there does not exist a standard mathematical for-mulation of âtheâ dynamic programming problem. >> /MediaBox [0 0 362.835 272.126] The solutions to these sub-problems are stored along the way, which ensures that each problem is only solved once. endobj xÚíXKoÜ6¾ûWè(¡Ã7)»9Ô"¨ÑØÙ´¤e-Ûª½T¢ÕÚI.ýëzPZÉ1ì¤(`±¢DgçEâà. The original contribution of Dynamic Economics: Quantitative Methods and Applications lies in the integrated approach to the empirical application of dynamic optimization programming models. Viewed 67 times 2. /Type /Annot /Subtype /Link Dynamic programming in macroeconomics. Behavioral Macroeconomics Via Sparse Dynamic Programming Xavier Gabaix March 16, 2017 Abstract This paper proposes a tractable way to model boundedly rational dynamic programming. /Subtype /Link /Rect [31.731 113.584 174.087 123.152] /A << /S /GoTo /D (Navigation37) >> /ProcSet [ /PDF /Text ] >> 97 0 obj >> /Type /Annot Appendix A1: Dynamic Programming 36 Review Exercises 41 Further Reading 43 References 45 2 Dynamic Models of Investment 48 2.1 Convex Adjustment Costs 49 2.2 Continuous-Time Optimization 52 2.2.1 Characterizing optimal investment 55 /Rect [31.731 125.012 238.815 136.701] /Rect [31.731 57.266 352.922 68.955] << /D [101 0 R /XYZ 9.909 273.126 null] << Later we will look at full equilibrium problems. What is Dynamic Programming? model will ârst be presented in discrete time to discuss discrete-time dynamic programming techniques; both theoretical as well as computational in nature. >> >> << << /Type /Annot endobj /Type /Annot Dynamic Programmingï¼the Problems Canonical Form Canonical Discrete-Time Infinite-Horizon Optimization Problem Canonical form of the problem: sup fx(t);y(t)g1 t=0 â1 t=0 tU~(t;x(t);y(t)) (1) subject to y(t) 2 G~(t;x(t)) for all t 0; (2) x(t +1) =~f(t;x(t);y(t)) for all t 0; (3) x(0) given: (4) âsupâ interchangeable with âmaxâ within the note. /Subtype /Link /A << /S /GoTo /D (Navigation4) >> 91 0 obj /Border[0 0 0]/H/N/C[.5 .5 .5] /Type /Annot >> The Problem. /Type /Annot /Rect [31.731 201.927 122.118 213.617] We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. /Type /Annot Dynamic Programming Dynamic programming is a useful mathematical technique for making a sequence of in-terrelated decisions. /Border[0 0 0]/H/N/C[.5 .5 .5] endobj This chapter provides a succinct but comprehensive introduction to the technique of dynamic programming. The main reference will be Stokey et al., chapters 2-4. 92 0 obj Skip to main content.sg. Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. The author treats a number of topics in economics, including economic growth, macroeconomics, microeconomics, finance and dynamic games. endobj Dynamic Programming in Economics is an outgrowth of a course intended for students in the first year PhD program and for researchers in Macroeconomics Dynamics. /Type /Annot /Subtype /Link it is easier and more efficient than dynamic programming, and allows readers to understand the substance of dynamic economics better. /A << /S /GoTo /D (Navigation11) >> /Subtype /Link >> /A << /S /GoTo /D (Navigation24) >> /Type /Annot Let's review what we know so far, so that we can start thinking about how to take to the computer. It can be used by students and researchers in Mathematics as well as in Economics. 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 0 $\begingroup$ I try to solve the following maximization problem of a representative household with dynamic programming. Try. endobj Simplest example: ânitely many values and ⦠/Type /Annot /Border[0 0 0]/H/N/C[.5 .5 .5] /A << /S /GoTo /D (Navigation33) >> endobj /Rect [31.731 188.378 172.633 200.068] Dynamic Programming in Python - Macroeconomics II (Econ-6395) Introduction to Dynamic Programming¶ We have studied the theory of dynamic programming in discrete time under certainty. >> endobj /Border[0 0 0]/H/N/C[.5 .5 .5] >> << /A << /S /GoTo /D (Navigation1) >> The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. 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