Art of Smooth Pasting

Name: Art of Smooth Pasting
Availability: InStock
ISBN: 9783718653843

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…

Book details

List price: $99.95
Copyright year: 1993
Publisher: Taylor & Francis Group
Publication date: 5/11/1993
Binding: Paperback
Pages: 92
Size: 5.91" wide x 8.43" long x 0.35" tall
Weight: 0.374
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