Federal State Educational Institution
state-funded institution of higher education
"FINANCIAL UNIVERSITY AT
GOVERNMENT OF THE RUSSIAN FEDERATION"
(Financial University)
Department of Mathematics
Viktor A. Byvshev
Mathematical modeling and quantitative research methods in management
Syllabus
For students studying under the
in the field of training 38.04.02 "Management",
Orientation of master’s degree programs:
"Corporate Governance",
Management and International Business"
1. Name of the discipline - Mathematical modeling and quantitative research
methods in management.
2. Mapping of learning outcomes (list of competences), with the relevant indicators described and subject learning outcomes indicated
The section lists the graduates’ coded competencies that are to be developed during
the learning process, indicators that show their development (generalized descriptions of specific actions performed by the graduate that clarify and reveal the competence content), learning outcomes (knowledge, skills) with indicators of competence development (in the form of a table):
Table 1
Competence
code
PKN-2
Competence
Ability toapply modern methods and
techniques of data
collection and analysis, as well as identification and forecasting of the main socio-economic objects
of management.
Learning outcomes (skills2,
Competence development in- and knowledge) and indicadicators1
tors that show competence
development
1. Develops methods, techKnow modernmethods and
niques and tools for analyzing tools for analyzing and preand predicting trends and so- dicting trends in time series of
cio-economic indicators.
socio-economic indicators.
Be able to build econometric
models of time series of socio-economic indicators.
2.They use tools for diagnos- Know the tools for diagnosing changes in the state of
ingя the state of management
management objectsat an
objectsя.
early stage in order to predict Be able to choose tools forя
the results of their activities
predicting the performance of
and prevent negative consemanagement objectsя.
quences.
3.Has the ability to analyze
Know the tools for predicting
the problems of the financial- theя financial- and economand economic state of organi- icя state of an organization.
zations and predict their con- Be able to build models for
sequences.
predicting the financial- and
economic state of an organization.
1
To be filled in when the updated Financial University educational standards and federal state educational standards of higher education
“3++” are implemented.
2 Skills are described when the Financial University educational standards of the 1st generation and federal state educational standards
of higher education “3+” are implemented.
2
UK-6
Ability tomanage a
project at all stages
of its life cycle.
4.Intelligentеinformation
technologies are used to improve the efficiency of
knowledge management.
Know intelligent information
technologies for predicting
the state of an organization.
Уметь выбирать Be able to
choose the application software depending on the tasks
being solved.ное программное обеспечение в зависимости от решаемых задач.
1.Applies basicproject planning tools проекта; in particular, forms a hierarchical structure of work, project schedule,
necessary resources, cost and
budget, plans procurement,
communications, project quality and risk management, and
more.
Know the basic mathematical
programming tools, used in
project planning.
Be able to use software products for project planning and
project risk management.
2.Manage project executors,
apply tools for monitoring,
maintainingя and managing
project changes, implement
measures to provide resources, distribute information, prepareе reports,
monitor and manage project
timing, cost, quality and risks.
Know the tools for preparing
project implementation reportsреализацииproject implementation reports.
Be able to apply tools for
preparing reports on реализации project implementation.
3. Place of the subject in the curriculum
Discipline "Mathematical modeling and quantitative research methods in management" refers to the third module B. 1. 1. 3 of disciplines that are invariant for the
direction of training, reflecting the specifics of the University. Discipline "Mathematical modeling and quantitative research methods in management" is based on the
knowledge gained in the framework of the basic disciplines:"Economic Theory and
Business Management", "Mathematics", "Economic Statistics", "Microeconomics",
"Macroeconomics","Strategic Financial Management".
4. Workload in credits and academic hours, with class work (lectures and
seminars) and self-study indicated
3
The data are presented in the form of the table 2.
Table 2
Total
(in credits and
hours)
3/108
32
8
24
76
Control work
Exam
Type of work
Overall workload
Class work
Lectures
Seminars, practicals
Self-study
Formative assessment
Summative assessment
Module 3
(in hours)
108
32
8
24
76
Control work
Exam
5. Subject content (with the thematic components indicated)
1. Mathematical modeling method in management, economics, and finance.
Financialand economic object and its mathematical model. Exogenous and endogenous variables of the economic and mathematicalой model. Descriptive and
optimization models. Optimizationproblems were presented in the form of linear
and nonlinear programming problems. The Lagrange method. Structural and reduced form of the model. Limit values and elasticity of endogenous variables of
the model.
2. Leontiev's input-output model for managing the production sector of the national economy.
CFinal, intermediate and final products. Technological coefficients. Cross-industry delivery model. Structural and reduced form of the Leontiev model. Leontiev's animator. Identity and cross-industry balance sheet table.
3. Game-theoretic models making managerial decisions.
Participants in the game (conflict) and their strategies. Situation and outcome of
the game. A zero-sum game. Payment matrix of the game. Normal form of the
game. Axiom of player behavior and algorithm for choosing their optimal strategies. The saddle point game and its solution. Non-zero-sum game and Nash equilibrium. Playing with nature in a situation of uncertainty and risk.
4. Regression models of financial-and economic objects and their construction scheme.
4
Regression model of a financial and economic object and its construction
scheme. Linear multiple regression model (basic model) and modelb as a system of simultaneous equations. Evaluation ofthe linearоmodel of multiple aggressions by the least squares method. Onthe estimation of a model as a system
of linear simultaneous equations by the two-step least squares method.
Forecasting based on the estimated regression model.
5. Structural models of time series and their useе for forecasting financial-and
economic indicators of management objects.
Time series and the structure of its levels. Additive and multiplicative time series
models. Models of t-rendsofthe oth and seasonal component. Estimationof the
structuralой model of a time series by the least squares method. Forecasting of
financial - and economic indicators of management objects using structural time
series models.
6. List of educational and methodological support for independent work of students in the discipline
6.1. List of questions assigned for independent mastering of the discipline,
forms of extracurricular independent work
Table 3
Itemized subject
content
Questions the students should answer within
the self-study process
Types of outof-class activities
Work with edTopic 1. Mathemati- 1. The object and itsmathematical model.
cal modeling method 2. Specification of the model, itsexogenous and en- ucational literature and disin management, eco- dogenous variables.
cuss questions
3. Optimization and descriptive models.
nomics and finance.
on the topic of
4. Structural and reduced form of the model.
Descriptive and opti- 5. Limit values of endogenous variables of the the
lesson.
Performing
mization models.
model and the rule for calculating them.
Limit values and elas- 6. Elasticity of endogenous model variablesли and home work on
the topic of the
ticity of endogenous a rule for calculating elasticity values.
lesson.
7. Lagrange method of transformation of the optivariables of the
mization model to the reduced form.
model.
8. The economic meaning of Lagrange multipliers.
Topic 2. Leontiev's input-output model for
managing the production sector of the
1. Gross, intermediate and final products of the industry.
2. Technological coefficients. 3. Modelof cross-industry deliveries. 4. Structural and reduced form of
5
Work with educational literature and discuss questions
on the topic of
economy.
Calcula- the Leontiev model. Leontiev's animator.
tions based on the Le- 5. Identity of intersectoral balance.
ontiev model for a 6. Cross-industry balance sheet table.
fragment of the manufacturing sector of
the Russian economy.
the lesson.
Performing
homework on
the topic of the
lesson.
Topic 3. Game-theoretic models of managerial decision-making.
1. Participants in the game (conflict) and their strategies.
2. Situation and outcome of the game.
3. A zero-sum game.
4. Payment matrix of the game and нnormal form
of the game.
5. Axiom of player behavior and algorithm for
choosing their optimal strategies.
6. The saddle point game and its solution.
7. Playing with nature in a situation of uncertainty
and risk.
Work with educational literature and discuss questions
on the topic of
the lesson.
Performing
homework on
the topic of the
lesson.
Topic 4. Regression
models of financial
and economic objects and their construction scheme.
1. Regression model of a financial and economic
object and its construction scheme.
2. Linear multiple regression model (basic model)
3. Model in the form of a system of simultaneous
equations.
4. Estimation of the linear model of multiple aggression by the least squares method.
5. Estimation of the model as a system of linear
simultaneous equations using the two-step least
squares method.
6.Forecasting based on the estimated regression
model.
1. Time series and the structure of its levels.
2. Plotting a time series.
3. Structuraladditive and multiplicative modelsь of
time series.
4. Models of the trend and seasonal components. 5.
Estimation of the structural model of a time series
by the least squares method.
6. Forecasting of financial and economic indicators
of management objects using structural time series
models.
Work with educational literature and discuss questions
on the topic of
the lesson.
Performing
homework on
the topic of the
lesson.
Topic 5. Structural
models of time series and their use
for forecasting financial and economic indicators of
management objects.
6
Work with the
educationalliterature
and
discuss questions on the
topic of the lesson.
Performing
home work on
the topic of the
lesson.
6.2. List of questions, tasks, and topics to prepare for the current control
1. Financialand economic object and itsmathematical model.
2. Exogenous and endogenous variables of the mathematical model.
3. Optimization and descriptive models.
4. Example of a model in the form of a linear programming problem.
5. Example of a model in the form of a nonlinear programming problem.
6. Structural and reduced form of the model.
7. Limit values of endogenous variables of the model and their calculation rule.
8. Elasticity of endogenous variables of the model and the rule for calculating elasticity values.
9. The economic meaning of Lagrange multipliers.
10. Leontiev's task is to manage the production sector of the national economy.
Gross, intermediate and final products of the industry.
11. Technological coefficients.
12. Cross-industry delivery model.
13. Structural form of the Leontiev model.
14. Thegiven form of the Leontiev model. The Leontiev multiplier and the economic
meaning of its elements.
15. Identity and cross-industry balance sheet table.
16. The concept of a game (conflict),in private players of the game and their strategies.
17. Situation and outcome of the game.
18. A zero-sum game.
19. Payment matrix of the game and the normal form of the game.
20. Axiom of player behavior and algorithm for choosing their optimal strategies.
21. The saddle point game and its solution.
22. Non-zero-sum game and Nash equilibrium.
23. Playing with nature in a situation of uncertainty.
24. Playing with nature in a risky situation.
25. Regression model of a financial and economic object and its construction
scheme.
26. Linear multiple regression model (basic model).
7
27.Estimation of a linear modelusing the least squares regression method.
28. Investigation of the properties of the residues of the linear regression model.
29. Checking the significance of the explanatory variables of the evaluated model.
30. Quality characteristics of the linear model of multiple regression.
31. Forecasting based on the estimated regression model.
31. Time series and the structure of its levels.
32. Plotting a time series.
33. Structural additive and multiplicative time series models.
34. Models of the trend component.
35. Seasonal component model. The concept of fictitious variables.
36. Estimation of the structural model of a time series by the least squares method.
37. Forecasting of financial and economic indicators of management objects using
structural time series models.
6.3. Examples of control work tasks
Example 1. The structural form of the Baumol-Tobin model for managing a firm's
current account is as follows:
𝑟
𝜑 = 𝑐 ∙ 𝑛 + ∙ 𝑚 → 𝑚𝑖𝑛
2
{
𝑚∙𝑛=𝑀
𝑚 ≥ 0, 𝑛 ≥ 0.
Here 𝜑 - total costs of the company for the maintenance of accounts, 𝑚 - value of
the balance of monetary funds on the account after its replenishment, 𝑛 - number
of refills account in the year, 𝑀 - required level of cash funds in the year (exogenous
variable), 𝑐 - value transaction costs in the replenishing of account (exogenous variable), r - norm alternative cost (exogenous variable).
It is required to determine the level of optimal costs of the company at c=0.1,
M=520, r=0.06.
Example 2. Using the data from Table 4, plot the quarterly levels of Russia's real
GDP (billion rubles in 2008 prices). Like the component is present in quarterly levels
Russia’s GDP? Make a specification of the structural model of this time series and
evaluate this model using the least squares method.
See Table 4. Quarterly levels of Russian GDP
Year
1995
I quarter
5355,0
II quarter
5523,1
8
III quarter
6030,0
IV quarter
6000,2
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
5235,1
5212,0
5134,7
5041,7
5617,6
5880,8
6104,2
6567,4
7042,9
7435,6
7978,3
8622,1
9413,2
8547,0
8894,9
9186,1
9620,6
9690,9
9745,8
9527,5
9275,3
9628,8
9758,0
5333,8
5289,7
5237,6
5402,6
5955,4
6256,1
6531,8
7052,3
7618,6
8076,7
8729,5
9481,8
10231,0
9090,1
9544,6
9859,0
10271,4
10390,6
10464,6
9978,4
9921,5
10490,3
10580,9
5698,1
5860,1
5343,0
5955,5
6583,6
6980,5
7289,7
7742,7
8309,8
8805,1
9526,3
10304,9
10965,6
10020,5
10403,9
10930,5
11265,6
11407,0
11504,7
10810,7
10763,5
11261,0
11281,8
5814,7
6024,9
5474,9
6136,3
6643,4
6945,0
7373,2
7942,6
8436,6
9093,0
9900,5
10809,9
10667,0
10391,0
10918,8
11482,2
11712,0
11956,0
12007,5
11284,3
11562,6
11578,9
Example 3. A farmer (player A) can sow one of three crops on his plot of land in
the current year: A1 - oats, A2 - rye, A3 – rice. The yield of each of these crops
depends on the weather (player B – nature), which can be in one of three states: B1
- dry, B2 - normal, B3 – rainy.
Average grain prices and their yield levels (yij) for each weather condition are
known and given in the following table.
9
Is required: choose the optimal sowing strategy of the farmer, assuming that there
is no additional information about possible weather conditions.
A note. A farmer's sowing strategy is considered optimal if it brings the farmer the
highest income in a certain sense.
7. Mandatory and optional reading list
7.1. Mandatory
1. Mathematical modeling and quantitative methods of research in management: a
textbook / M. Yu. Mikhaleva.М. Ю. Mikhaleva, I. V. Orlova Street. - Moscow: University textbook: INFRA-M, 2018 – - EBS Znanium.com. - URL: http://znanium.com/catalog/product/948489 (accessed: 05.11.2019). - Text: electronic.
2. Mikhaleva M. Yu., Orlova I. V. Practicum on the discipline "Mathematical modeling and quantitative methods of research in management". - Moscow: Financial
University, Departmentof Data Analysis, Decision-making and Financial Technologies, 2018. - 213 p. - IOP of the Financial University. - URL: https://portal.fa.ru/Files/Data/fe05984c-32da-4b53-9efc-f6fc1ec51bb1/Pract_Matmodelir_mMen_18.pdf (дата обращения: 05.11.2019). - Text: electronic.
3. Byvshev V. A., Mikhaleva M. Yu. Practicum on the discipline "Modeling of microeconomic processes", Moscow: Financial University, Department of Data Analysis, Decision-making and Financial Technologies, 2019, 51 p.
4. Babeshko L. O., Beach M. G., Orlova I. V. Econometrics and econometric modeling: Moscow, University textbook: INFRA-M, 2018, 385 p –
10
5. Byvshev V. A. Workshop Econometrics in R: Time Series Models: Collection of
exercises and tasks for independent work of students in the disciplines "Econometrics", "Econometric research", "Applied methods and models of regression analysis"
for students studying in the areas of training 01.03.02. "Applied Mathematics and
Computer Science" (bachelor's degree program), 38.03.01 "Economics" (master's
degree program), 01.04.02 "Applied Mathematics and Computer Science" (master's
degree program). Moscow: Financial University, Department of Data Analysis, Decision making and Financial Technologies, 2019. - 110 p.
7.2. Optional
1. Fundamentals of mathematical modeling of socio-economic processes. Practicum
/ M. G. Beach, I. V. Orlova, G. V. Ross [et al.]. – MOSCOW: Kompany KnoRus,
2019. – 292 p. – ISBN 9785406070345.
8. List of IT resources, incl. the list of software, information and reference systems (as appropriate)
8. 1. Software:
1. Windows OS.
2. Microsoft Office software.
8.2. Databases and information and reference systems
1. Information and educational portal of the Financial University http://portal.ufrf.ru/.
2. Digital Resources Library of the Financial University: http://elib.fa.ru/
8.3. Certified software/hardware used for data protection
ESET Endpoint Security antivirus software.
11