probset10

probset10 - \documentclass[12pt]cfw_article...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
\documentclass[12pt]{article} \usepackage{amsmath} \usepackage{geometry} \usepackage{url} \geometry{top=1in,bottom=1in,left=1in,right=1in} \setlength{\parindent}{0in} \setlength{\parskip}{2ex} \begin{document} \begin{center} \begin{tabular*}{6.5in}{l@{\extracolsep{\fill}}r} \multicolumn{2}{c} {\bfseries Problem Set 10} \\ \multicolumn{2}{c} {Due Tuesday, November 24} \end{tabular*} \end{center} {\bfseries 1. Linear-Quadratic Dynamic Programming} This problem will give you more practice with dynamic programming under certainty; it presents another case in which an explicit solution for the value function can be found using the guess-and-verify method. The problem is to choose sequences $\ {z_{t}\}_{t=0}^{\infty}$ for a flow variable and $\{y_{t}\}_{t=1}^{\infty}$ for a stock variable to maximize the objective function $$ \sum_{t=0}^{\infty} \beta^{t} (Ry_{t}^2+Qz_{t}^{2}), $$ subject to the constraints $y_{0}$ given and $$ Ay_{t}+Bz_{t} \geq y_{t+1} $$ for all $t=0,1,2,. ..$, where $\beta$, $R$, $Q$, $A$, and $B$ are constant, known parameters. This problem can be described as being ``linear-quadratic,'' because the constraint is linear and the objective function is quadratic. The discount factor lies between zero and one, $0<\beta<1$, and to make the objective function concave, it is helpful to assume that $R<0$ and $Q<0$ as well. \begin{description} \item a. Write down the Bellman equation for this problem. \item b. Now guess that the value function also takes the quadratic, time-invariant
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

probset10 - \documentclass[12pt]cfw_article...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online