Quantitative Dynamics » Books

Uncertainty in Making Decisions (SPbSTU Press, 2005)

Olga — Sun, 24 Apr 2005 01:24:14 +0000

New edition of the lecture textbook. Main types of models used in the decision-making theory are presented with examples from business practice. The principle attention is paid to the problem of selection of useful information in decision-making process and solving the associated inverse problems. The contents are similar to the 1999 edition.

O. Y. Uritskaya. Making Decisions under Risk and Limited Information Conditions // St. Petersburg: SPbSTU Press, 2005, 108 p.

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Fig. 1. Process transformation of data to the information. Preceding throw the physical, semantic and pragmatic filters significant part of important information can be lost with statistical and semantic noise or is not recognized as useful one.

Fig. 2. Antagonistic Game. If participants have the opposite goals, they can not negotiate and they have to hide information form each other, because in this case the gaincan be increased only if the opponent makes a mistake. The solution shown is most cautious one. In literature it calls pessimistic approach. But if your opponent is your enemy you have no other choice. The classic example of this game at the practice is gaining a new part of stable market. If you get it, somebody has to loose. But in real life this happens very rare, markets are use to grow and the opponents are not your real enemy, just partners with different goals and negotiation always is good solution.

Fig. 3. Bimatrix Game. For more reasonable choice than just guessing we usually ask for help from professionals. They are people, so have their own goals and interests in the situation. Result – the goals are not opposite, but just different and model become Bimatrix game. This name is used for 2 person games, if more is consider more – it just become too complicated to demonstrate in matrix form, but approach is good for any number of participants. Here everyone is interested in max gain, but have to choose depend on moving of other participant. In this particular example they probably never choose right strategy if only will not negotiate. In this case they can share they profit or some benefits. Here we still have some option to increase the gain with new inf from our opponent. What why the always pays off.

Planning at the company (SPbSTU Press, 2005)

Olga — Sun, 24 Apr 2005 01:13:36 +0000

The main types and organizing forms of companies, their structure, management and planning problems are considered. Examples of mistakes and successes of behavior and decisions at the markets are discussed. Main attention is paid to principles of organizing, financing and management of the company. The textbook is created for M.A. graduate students specializing in economics, management and business areas.

O. Y. Uritskaya. Organizing and planning at the company // St. Petersburg: SPbGTU Press, 2005, 236 p.

Annotation and contents (in Russian)

Fig.1 The Blake Mouton model.

Risk Evaluation in Economic systems (SPbSTU Press, 2005)

Olga — Mon, 11 Apr 2005 22:52:09 +0000

A new lecture textbook for МА specializing in economics, mathematical and quantitative methods, macroeconomics and monetary economics. Basic forms of economic system stability and new quantitative methods and approaches to its are considered. Main attention is paid to issues of amount and sufficiency of information in the system. Novel approaches to forecasting and simulations of complex economic systems dynamics and their application examples are presented.

O. Y. Uritskaya. Stability and Risk Evaluation in Economic systems // St. Petersburg: SPbGTU Press, 2005, 171 p.

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Fig. 1. Examples of fluctuations in daily average exchange rates in the economic systems with different levels of stability: Russian ruble, Brazilean real, Indonesian rupia and European Currency unit.

Fig. 2. Classification of currency exchange rate fluctuations based on the estimation of DFA exponents ₁(4–30 days) and ₂(30–90 days). According to the efficient market hypothesis, the point ₁ = ₂ =1.5 corresponds to the optimal state of the national currency system with maximum long-term stability of the exchange rate. The countries were grouped according to the values of  parameters: N – Economically developed countries: Great Britain, Greece, EU, Canada, New Zealand, Norway, USA, Swiss, Japan, Australia; D – Developing countries with relatively stable monetary systems: Israel, Columbia, Chili, South Africa; H and L – Unstable Developing countries, prior to crises: Bulgaria, Brazil, India, Kazakhstan, Mexico, Russia, Rumania, Turkey, Ecuador; А – Unstable Developing Asian countries before the 1997 monetary crisis: Indonesia, Malaysia, Singapore, Thailand, Taiwan, Philippines, South Korea; М – Marginally stable, Countries from groups Н, L and А after crises.

Fig. 3. An example of a time series from the group N (US dollar against the German mark), showing variations in the fractal indices ₁ and ₂ in the range of 1.25 to 1.75. Index ₂ does not cross these critical levels for 30 years.

Contents

Lecture 1. Economic Risk and Economic Information.

The reasons for appearance of risks in economics. Difficulties of scientific research in economics. Content and classification of economic information.

Lecture 2. Characteristics of the Economic Systems.

System essence of economic objects. Main system principles. The large interactive systems. System analysis.

Lecture 3. Stability of an Economic System.

Stability of an economic system; critical conditions and crises. Forms of economic system stability. The history of investigation of the equilibrium in economics. Self-organized nature of dynamical equilibrium.

Lecture 4. Mathematical Modeling of Economic Systems.

“Mathemazation” in science. Deterministic and stochastic models. Problems of complex system modeling. History of mathematical modeling in economics. Holistic approach to simulations.

Lecture 5. Preparing and Processing Economic Data

The problem of selecting economic system state variables. Direct economic observations. Economic time series. Requirement to economic time series. Fluctuations of economic indices.

Lecture 6. Time Series Analysis

History of time series analysis. Generated, deterministic and stochastic time series. Fluctuations and bifurcations in time series. Problem of management in the complex economic system.

Lecture 7. The Theory of Self-Organized Criticality.

Mechanisms of catastrophes in complex systems. Reasons of local instability and global stability of the complex system. Physical model. Fractal structure of time series produced by complex interactive systems.

Lecture 8. Fractals and Their Properties.

Fractional dimension. Scale invariance. Self-similarity. Geometric fractals. P.Bak’s theorem of complex equilibrium.

Lecture 9. Methods of Fractal Time Series Analysis.

Estimation of the fractal dimension of time series. Geometric and statistical methods of fractal dimension estimation and their comparative characterization.

Lecture 10. Forecasting Fractal Dynamics.

Modeling of stochastic processes. Efficient market hypothesis. Forecasting time series behavior. Interpretation of fractal analysis results. Persistent and anti-persistent behavior of economic processes. Using fractal analysis for system stability evaluation. Sub- and super-critical conditions of unstable complex system evolution.

Lecture 11. The Risk Factors in the Macroeconomic Systems.

The world facilities as a system. The world trade, the international migration of the production’s factors. International exchange and financial relations. The international economic integration.

Lecture 12. The World Currency System. The Exchange Rates.

The international exchange system and its evolution. Nominal and real exchange rates. Floating and fixed exchange rates. The devaluation and revaluation. The international exchange market.

Lecture 13. The Macroeconomic System’s Classification by the Level of Dynamical Stability.

Fractal analysis of currency time series. Classification of the currencies by the stability groups. Recovering of system stability after the economic crisis.

Lecture 14. Evaluating Economic System Stability.

Methodology of evaluation of exchange rate volatility by logarithmic returns. Comparison of volatility values of stable and unstable floating exchange rates. Optimal intensity of exchange rate fluctuations

Lecture 15. Modeling Characteristics of Active Phase of Economic Crisis.

Determination of normal range of nonstationary fluctuations of Peng’s critical exponent. Evaluating time series fractal structure Evaluation of accumulated deviation of Peng’s exponent beyond the normal range and its relation to crisis magnitude and duration. Fractal regression of monetary crashes.

Lecture 16. Estimating Risks by Statistical Methods.

Standard probabilistic and statistical methods for risk estimation and their inherent limitations. Risk Levels. Risk Factors. Risk Scales.

Lecture 17. Estimating Economic Risks by Fractal Methods.

Quantitative risk assessment by fractal methods. Pareto exponent and its economic interpretation. Examples of financial risk estimation by the Pareto exponent technique.

Lecture 18. The Methods of Economic Risk Reduction.

The main methods of reduction of the risk in economic systems. Insurance, standby, limiting, diversification and hedging as instruments of the reduction of the economic risk.

Problems

Problem 1. Estimation of the fractal dimension of time series by ruler method. Forecast and risk evaluation.

Problem 2. Quantitative risk assessment by fractal method. Insurance risk evaluation.

Training session. Computer game “Stock market tactics”: description and trading examples.

Economic Risk Theory (SPbSTU Press, 1999)

Olga — Sun, 11 Apr 1999 01:59:11 +0000

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 holistic modeling of stochastic economic system behavior and problems of quantitative estimation of economic risks.

The textbook is designed for students of economic, marketing, management departments and for everyone who is interested in the problem of risk analysis in complex economic systems.

O. Y. Uritskaya. Introduction to Economic Risk Theory: Lecture Textbook // St. Petersburg: SPbSTU Press, 1999.

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Fig. 1. An example of bifurcation in model time series.

Fig. 2. Mont

hly fluctuations in world prices for gold (top) and the corresponding simulated cycle. (Cycles, 1993).

Fig. 3. Dependence of the form of the Pareto distribution tail on the Pareto index value.

Contents

The subject of economic risk theory
1. Origin of risk in economic system
2. Characteristics of economic systems
3. Modeling of economic processes
4. Time series analysis
Basis of economic risk theory
1. Self-organized criticality theory
2. Self-organized criticality models
3. Fractals and their properties
4. Fractal objects
5. Fractal properties of economic systems
Methodology of economic risk theory
1. Economic risk estimation
2. Data preparation (measurements, aggregation, calendar problems)
3. Fractal dimension of time series (ruler method, box counting statistics, correlation function method, spectral method, Hurst rescaled range analysis)
4. Forecasting long-term tendencies on the base of time series fractal dimension
5. Analysis of system stability and catastrophe forecasting
6. Risk estimation by statistical methods
7. Risk estimation by fractal methods
Problems

Decision making theory (SPbSTU Press, 1999)

Olga — Mon, 05 Apr 1999 02:26:06 +0000

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), risk or uncertainty condition (game theory) and partial information condition (statistical games or games against Nature). Analysis and solution examples in business-related tactical and strategic problems are presented. Major attention is devoted to the ways of formalization, modeling and interpretation of analysis results and solutions. In particular, the poser of method’s adaptability and its restrictions are discussed. Textbook is designed for students of economic, marketing, management departments and for everyone who is interested

O. Y. Uritskaya. Decision-Making Theory: Lecture Textbook // St.Petersburg: SPbSTU Press, 1999.

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Fig. 1. Decision-making (DM) as a process is much longer than we use to believe.

Fig. 2. Decision-making results refer not to the initial problem, but to formalized model of situation, which was built using only information available at the moment.

Fig. 3. Sensitivity to information. Process transformation of data to the information. Preceding throw the physical, semantic and pragmatic filters significant part of important information can be lost with statistical and semantic noise or is not recognized as useful one.

Fig. 4. Classification of DM models. Choosing wrong model of situation leads to the critically wrong results.