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 — ''Itô'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 economics.
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 de

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