Economic and Mathematic Modeling
The Course is the advanced course that is dedicated to studying the fundamental and applying basis of mathematical modeling of economic systems. The fundamental distinguishing feature of this course comparing with the traditional analogues that are limited with studying the equilibrium models and quasistatic transitions is a priority in studying non-equilibrium economic systems. The mathematical tools of modern non-linear dynamics are used for modeling such systems. The mathematical tools that are represented in the course are the compact set of methods that allow to efficiently analyze models of economic processes. Studying the determined dynamic systems ends with a studying the basics of dynamic chaos theory. It’s a logical transition from the determined systems to stochastic systems, defining the logical integrity of the course.
The topic of the course that is dedicated to the stochastic systems is preceded with the overview of empirical data of stock market fluctuations. Such fluctuations can be described with Levy’s distribution, that plays such a sufficient role in economics as the Gauss’s one in natural sciences. Much attention is paid to the problem of random walk, especially the Levy’s flights. The topic “Minority Games” stands apart, where the transition from the stochastic behavior of objects and subjects of economics to the dynamic one.Studying of every topic starts with a review of a real economic problem with a further mathematical model compilation and exploring of the mathematical tools used in it. The basics of qualitative and quantitative analysis of such models are also going to be studied.