Outlines of a lecture course of advanced Economic Risk Theory created for M.A. graduate students specializing in economics, management and business areas. The lecture course summarizes an 8-years experience in adapting and clarifying for economists a number of complicated math theories are presented such as catastrophe theory, fractal theory and fractal analysis techniques. The course
Results of fractal analysis of currency exchange rate fluctuations in several groups of countries with different financial and economical systems during the period 1995-2000 are presented. We demonstrate that the C. K. Peng’s detrended fluctuation analysis can be used as a sensitive tool for identifying inflation trends and revealing unstable regimes in currency dynamics over
In this project, we investigated fractal properties of temporal fluctuations of the volume of income taxes collected in St.Petersburg, Russia in 1996-1997. Time series of tax inflows typically consist of periodic and stochastic components. We show that the main periodic component, which represents the 30-day economic cycle, is strongly influenced by random fluctuations. We estimated
The modern approaches to forecasting critical conditions and catastrophic events in complex economic systems are introduced. Examples of application of quantitative methods of the economic risk theory to analysis of stability and diagnostics in economic systems based on statistical and/or nonlinear processing of time series are represented. The main attention is devoted to ways of
Modern mathematical methods and approaches to solving various applied problems in frames of the general decision making theory are considered. The decision making theory deals with the process of optimal alternative selection from a set of possible alternatives and corresponding models. Exposition includes types of conditions for making the decision: full information condition (criteria analysis),
A new approach to an investigation and modeling of dynamical systems in the economics is considered. Using a cellular automaton model, we show that stock markets, as complex systems with many coupled degrees of freedom, can operate in a stationary critical state associated with the regime of self-organized criticality (SOC). It is suggested that SOC
New diagnostics and modeling approaches for dynamic processes of economics have been considered. It has been shown that most of economic variables exhibit complex fractal temporal behavior rather than simple trends or cycles implied by traditional approaches of economic time series analysis. Fractal analysis indices are suggested that allow to obtaining valuable information about degree
