| Mathematical Economics I
E624 | 1660 | Chang
"Dynamic Economics under Uncertainty"
This is an introductory course to stochastic control theory with
applications to economics. The focal point of the mathematical
technique is the stochastic dynamic programming method. We shall go
through the essential elements of Ito's calculus (Wiener process,
stochastic integrations and Ito's lemma), the stochastic differential
equations (existence, uniqueness, and some closed-form solutions), and
the stochastic Bellman equations. Then we apply stochastic
optimization methods to several economic problems. The emphasis of the
course is on problem solving, not on proving general theorems. One of
the objectives is that you will be able to apply the Bellman equation
to dynamic economic problems the same way you apply the Lagrange
Multiplier method to static economic problems.
Applications to economics are many and selective. We will cover the
traditional optimal growth theory, including the inverse optimal
method. We will also cover adjustment cost theory of supply, optimal
consumption and portfolio rules, and, naturally, the one and only
Black-Scholes option pricing theory. Another class of problems will be
dealt with in this class is the one associated with "barriers." We
shall build our absorbing barrier theory based on the famous
Baumol-Tobin transactions demand for money model.
There is no text for the course. However, Malliaris and Brock's
(1982) Stochastic Methods in Economics and Finance should serve as an
excellent beginner. We follow a reading list of classic works and
research papers, some of which are prepared in my lecture notes. The
requirement for the course is a midterm exam and the final exam.