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Art of Smooth Pasting

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ISBN-10: 3718653842

ISBN-13: 9783718653843

Edition: 1993

Authors: A. Dixit

List price: $99.95
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Description:

The main mathematical ideas are presented in a context with which economists will be familiar. Using a binomial approximation to Brownian motion, the mathematics is reduced to simple algebra, progressing to some equally simple limits. The starting point of the calculus of Brownian motion -- "Ito's Lemma" -- emerges by analogy with the economics of risk-aversion. Conditions for the optimal regulation of Brownian motion, including the important, but often mysterious "smooth pasting" condition, are derived in a similar way. Each theoretical derivation is illustrated by developing a significant economic application, drawn mainly from recent research in macro-economics and international…    
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Book details

List price: $99.95
Copyright year: 1993
Publisher: Routledge
Publication date: 1/1/1993
Binding: Paperback
Pages: 92
Size: 5.50" wide x 8.50" long x 0.25" tall
Weight: 0.286
Language: English

Introduction to the Series
Preface
Brownian Motion
Random Walk Representation
Ito's Lemma
Geometric Brownian Motion
Some Generalizations
Discounted Present Values
Present Values for Exponential and Polynomials
Present Values for Powers of Geometric Brownian Motion
A Basic Differential Equation for Present Value
Derivation by Discrete Approximation
The General Solution
Differential Equation for Geometric Brownian Motion
General Diffusion Processes
Barriers
The Basic Differential Equation
Geometric Brownian Motion
Stopping
Resetting
Reflection
Example: Price Ceiling
Example: Exchange Rate Target Zones
Transitional Boundary
Example: Temporary Suspension
Optimal Control and Regulation
Stopping
Example: Irreversible Investment
Convex Costs: Continuous Control
Lump-Sum Costs: Impulse Control
Example: Menu Costs
Linear Costs: Barrier Control
Some Geometry and Intuition
Example: Competitive Industry
Generalizations
Mean-Reverting Processes
Finite Horizon
Some Characterization of Optimal Paths
Short Run: Time Until First Action
Long Run: Stationary Distribution and Average Action
Dynamics of Brownian motion: Kolmogorov Equations
References
Index