Economic and Mathematic Modeling

Prerequisites:

• Basic computer science principles and skills
• Basic economic systems principles and skills

Courses:

• System Analysis&Organization Design

Economic and Mathematical Modeling is the study of the stochastic and dynamic economic systems. Economic and Mathematical Modeling is the application of mathematical methods to represent theories and analyze problems in economics. Much of economic theory is currently presented in terms of mathematical economic models. Course is focused on understanding the role of mathematic modeling for quantitative analysis of stochastic and dynamic economic systems. Course content includes random walk theory, stochastic process theory, dynamic systems theory and dynamic chaos theory. In the lab part of the course the students can try different mathematic modeling software tools.

Topics include:

1. Stochastic systems.

1.1. Random walk. Levy stochastic processes.

1.2. Scales in financial data.

1.3. Stationarity and time correlation. Time correlation in financial time series.

1.4. Stochastic models of price dynamics.

1.5. ARCH and GARCH processes.

1.6. Financial markets and turbulence.

1.7. Correlation and anticorrelation between stocks.

2. Dynamic systems.

2.1. Mathematical Aspects of Dynamic Systems.

2.2. Multiple Equilibria and Structural Changes in Economic Systems.

2.3. Mathematical Aspects of Economic Cycles.

2.4. Economic Chaos in Deterministic Systems.

2.5. Urban Pattern Formation Process - Stability, Structural Changes and Chaos.

2.6. The Haken Slaving Principle and Time Scale in Economic Analysis

1. Mantegna R.N., Stanley H.E. An Introduction to Econophysics, Correlation and Complexity in Finance. Cambridge University Press, 2000.

2. Zang W.B. Synergetic Economics. Time and Change in Nonlinear Economics. Springer, 1991

3. Ian Jacques. Mathematics for Economics and Business. Pearson, 7 edition, 2012.  

4. Kenneth Shaw. Mathematical Modeling in Business and Economics: A Data-Driven Approach. Business Expert Press, September, 2014 (preview is available)