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# dynamic optimization economics lecture notes

The most common dynamic optimization problems in economics and ﬁnance have the following common assumptions • timing: the state variable xt is usually a stock and is measured at the beginning of period t and the control ut is usually a ﬂow and is measured in the end of period t; • horizon: can be ﬁnite or is inﬁnite (T = ∞). Economics 2010c: Lecture 1 Introduction to Dynamic Programming David Laibson 9/02/2014 . 1 The Basics of Dynamic Optimization The Euler equation is the basic necessary condition for optimization in dy-namic problems. First, I present intuitive derivations of the first-order necessary conditions that characterize the solutions of basic continuous-time optimization problems. We will start by looking at the case in which time is discrete (sometimes called Dynamic Optimization and Optimal Control Mark Dean+ Lecture Notes for Fall 2014 PhD Class - Brown University 1Introduction To ﬁnish oﬀthe course, we are going to take a laughably quick look at optimization problems in dynamic settings. In our lecture, we will consider … The Nature of Optimal Control In static optimization, the task is to –nd a single value for each control variable, such that the objective function will be maximized or minimized. Discrete time methods (Bellman Equation, Contraction Mapping Theorem, and Blackwell’s Suﬃcient Conditions, Numerical methods) • Applications to growth, search, consumption, asset pricing 2. Dynamic Optimization and Macroeconomics Lecture 3: Introduction to dynamic programming * LS, Chapter 3, “Dynamic Programming” PDF . Lecture 6: Discrete-Time Dynamic Optimization Yulei Luo Economics, HKU November 13, 2017 Luo, Y. Growth Model in Continous Time • Preferences: repres they are members of the real line. Second, I show why very similar conditions apply in deterministic and stochastic environments alike. Lecture 3: Growth Model, Dynamic Optimization in Continuous Time (Hamiltonians) ECO 503: Macroeconomic Theory I Benjamin Moll Princeton University Fall 2014 1/16. (Economics, HKU) ECON0703: ME November 13, 2017 1 / 43 . Outline of my half-semester course: 1. Continuoustimemethods(BellmanEquation, BrownianMotion, … Dynamic Optimization Problems 1.1 Deriving rst-order conditions: Certainty case We start with an optimizing problem for an economic agent who has to decide each period how to allocate his resources between consumption commodities, which provide instantaneous utility, and capital commodities, which provide production in the next period. Here we discuss the Euler equation corresponding to a discrete time, deterministic control problem where both the state variable and the control variable are continuous, e.g. Lecture 4: Applications of dynamic programming to consumption, investment, and labor supply [Note: each of the readings below describes a dynamic economy, but does not necessarily study it with dynamic programming. Dynamic Optimization in Continuous-Time Economic Models (A Guide for the Perplexed) ... of these notes is twofold. Plan of Lecture Growth model in continuous time • Hamiltonians: system of diﬀerential equations • Phase diagrams • Finite diﬀerence methods and shooting algorithm 2/16.