Art of Smooth Pasting

This book aims to widen the understanding 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 mathematical treatment of the subject.The main mathematical ideas are presented in a context which with which economists will be familiar. Using a binomial approach 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.