E624 | 1717 | Prof. Chang

E624 Mathematical Economics I "Stochastic Optimization in Continuous Time" by Professor Fwu-Ranq Chang This is an introductory course on stochastic control theory with applications to economics. The focal point of the mathematical technique is the stochastic dynamic programming method. It includes 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. These mathematical results will be integrated with 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, irreversible investment, exhaustible resources, optimal consumption and portfolio rules, index bonds, uncertain lifetimes and life insurance, and, naturally, the one and only Black-Scholes option pricing theory. Another class of economic applications will be covered in this course is the "barrier" problem. We shall build our absorbing barrier theory based on the famous Baumol-Tobin transactions demand for money model. The "text" for the course is the manuscripts that I have prepared. It is part of a book project, which so far has six chapters (about 200 pages) typeset in Scientific Word 2.5. They are: Chapter one: Probability Theory Chapter two: Wiener Process Chapter three: Stochastic Calculus Chapter four: Stochastic Dynamic Programming Chapter five: How to Solve It Chapter six: Barrier and Uncertain Lifetimes There will be a midterm exam and the final exam.