- The main objective of the Course is to present, examine and discuss with students fundamentals and principles of economic and mathematic modeling. This course is focused on understanding the role of mathematic modeling for quantitative analysis of economic systems. Generally, the objective of the course can be thought as a combination of the following constituents: 1) understanding of the role of mathematic modeling in financial and economic modeling, 2) obtaining skills in utilizing different mathematical techniques in economic problem solving, 3) familiarizing with different models of real-life problems in the economics.
- know main notions of the networks, multicriterial models, optimization problems and inventory management, matchings and financial models
- acquire skills of analyzing and solving economic and mathematic problems
- gain experience in economic and mathematic modeling
- IntroductionMathematics as a language for description of economics. Examples of real life applications and projects, i.e. assessment of the consumer basket of large retailers, analysis of customer outflow from the retail network, efficiency of bank branches, location of branches of a firm, analysis of living conditions in settlements and regions, etc.
- NetworksNetworks as a way to model restrictions on information exchange and interaction. Dissemination of information and influence in networks. Decision-making and strategic behavior of players in network interaction. Market analysis taking into account the network structure of connections. Classic centrality measures in networks. New centrality measures. Application of indices to migration processes, conflict networks, foreign claim networks, students’ mobility networks, etc.
- Multicriterial modelsQuantitative and qualitative characteristics (criteria). Pareto optimality. Methods for solving multi-criteria problems. Method of the leading criterion. Method of consecutive concessions. Reducing multi-criteria problems to single-criteria problems (scalarization). Goal programming. The method of threshold aggregation. Evaluation of the contribution of workers by the method of threshold aggregation.
- Optimization modelsBasic concepts of a static optimization problem. Instrumental variables, the objective function. The global and local maxima. Sufficient condition for the existence of a global maximum. Formulation of the linear programming problem (LP). Some special linear programming tasks (transport, production, etc.). Linear programming in MS Excel. The DEA analysis (data envelopment analysis). The construction of the efficiency frontier. Evaluating the effectiveness of firms, banks, and universities.
- Inventory managementRole of Demand in the development of inventory. Static Economic-Order-Quantity (EOQ) Models. EOQ with price breaks. Multi-item EOQ with storage limitations. Dynamic EOQ Models. Introduction of probabilistic inventory models.
- MatchingsMatchings and participants' preferences in the form of linear orders. Stable matchings. The Gale-Shapley algorithm. Personnel management and employment problems. Multi-criteria models for constructing matchings.
- Financial modelsTime value of money: future value and different schemes of compounding, perpetuities, annuities, effective annual rates. Present value and discounting. Cash flows. Bond features and prices. Portfolios of two risky assets. The Markowitz portfolio optimization model: security selection, capital allocation and the separation property. The CAPM model. Futures and options trading. Option versus stock. Financial crises. Taleb’s Black swans. Poisson processes. Models with stimulation and education. Hawkes models for crises prediction. ETAS model.
- Home assignmentsHome assignments should be done by students individually
- Final examinationThe examination shall be held in writing (test) with the use of asynchronous proctoring on the StartExam platform. StartExam is an online platform for conducting test tasks of various levels of complexity. The link to pass the exam task will be available to the student in the RUZ. Asynchronous proctoring means that all the student's actions during the exam will be “watched” by the computer. The exam process is recorded and analyzed by artificial intelligence and a human (proctor). Please be careful and follow the instructions (https://elearning.hse.ru/en/student_steps/) clearly!
- Aleskerov F., Bouyssou D., Monjardet B. ‘Utility Maximization, Choice and Preference’, Springer Verlag, Berlin, 2007
- Aleskerov, F., & Subochev, A. (2016). Matrix-vector representation of various solution concepts.
- Aleskerov, F., Meshcheryakova, N., & Shvydun, S. (2016). Centrality measures in networks based on nodes attributes, long-range interactions and group influence.
- Dempsey, M. (2020). Investment Analysis : An Introduction to Portfolio Theory and Management. London: Routledge. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2278900
- Taha H.A. Operations Research: An Introduction, 10-th Edition, Pearson Education Limited, 2017. – 849 p. – ISBN: 9781292165561
- Aleskerov, F. T., Chistyakov, V. V., & Kalyagin, V. A. (2010). Social threshold aggregations. Social Choice & Welfare, 35(4), 627–646. https://doi.org/10.1007/s00355-010-0454-9
- Aleskerov, F., Meshcheryakova, N., Nikitina, A., & Shvydun, S. (2018). Key Borrowers Detection by Long-Range Interactions.
- Aleskerov, F., Meshcheryakova, N., Rezyapova, A., & Shvydun, S. (2018). Network analysis of international migration.
- Hull, J. C. (2017). Options, Futures, and Other Derivatives, Global Edition. [Place of publication not identified]: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1538007