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. In our lecture, we will consider … Plan of Lecture Growth model in continuous time • Hamiltonians: system of differential equations • Phase diagrams • Finite difference methods and shooting algorithm 2/16. Lecture 3: Growth Model, Dynamic Optimization in Continuous Time (Hamiltonians) ECO 503: Macroeconomic Theory I Benjamin Moll Princeton University Fall 2014 1/16. 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. We will start by looking at the case in which time is discrete (sometimes called they are members of the real line. Dynamic Optimization and Macroeconomics Lecture 3: Introduction to dynamic programming * LS, Chapter 3, “Dynamic Programming” PDF . 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. 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. Outline of my half-semester course: 1. Lecture 6: Discrete-Time Dynamic Optimization Yulei Luo Economics, HKU November 13, 2017 Luo, Y. Growth Model in Continous Time • Preferences: repres 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. 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. Continuoustimemethods(BellmanEquation, BrownianMotion, … First, I present intuitive derivations of the first-order necessary conditions that characterize the solutions of basic continuous-time optimization problems. Second, I show why very similar conditions apply in deterministic and stochastic environments alike. (Economics, HKU) ECON0703: ME November 13, 2017 1 / 43 . 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 = ∞).
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