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
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
General
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