The Art of Smooth Pasting

This book aims to widen the understanding and use of stochastic dynamic choice and equilibrium models. It offers a simplified and heuristic exposition of the theory of Brownian motion and its control or regulation, rendering such methods more accessible to economists who do not require a detailed, rigorous mathematical treatment of the subject. The main mathematical ideas are presented in a context with which economists should 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 macroeconomics and international economics.