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.