Goal of research: problems of optimization modeling, multi-criteria decision-making, social chose theory, models of data analysis and forecasting, as well as the application of the developed models and methods in applied problems of socio-economic analysis, political science, in the financial and banking spheres.
Methodology: methods of multi-criteria decision-making, methods of game theory and optimization modeling, methods of individual and social choice theory, methods of statistic, network and cluster data analysis, methods of probability theory, methods of belief functions theory and others.
Empirical base of research: data on the transport system of part of Russia, data on the financial condition of 192 shipping companies in 36 countries around the world for the period 2001-2016, S&P500 stock index data and the USD/RUB currency pair data, data on the recommendations of financial analysts on the prices of shares of Russian companies for the period 2010-2016, data on migrant flows collected UN Population Division, World Bank International Trade Data, open data on the resources and benefits of the Arctic region, data of The Global Innovation Index 2013-2016.
Results of research:
- a mathematical model is proposed of location of transport nodes with access roads in a regional transport system, taking into account the existing transport system of the region; optimization problem (in the case of known prices for transportation and construction) and robust problem (exact values of prices are not known) are formulated on the basis of the presented model; both problems were tested on data on the transport system of part of Russia;
- the results of the modification of the previously developed mathematical model of investing in a project for the construction of plants for the processing of solid domestic waste into biomass used as fuel in power supply and heating systems as a three-persons game are presented; the possibility of finding Nash equilibria of this game is proved;
- a mathematical model has been developed, and the problem of estimating the cost of installing stations for charging electric vehicles on highways has been formulated under linear constraints; it has been proven that the optimum can be found by solving an auxiliary mathematical programming problem with mixed variables;
- within the framework of modeling preferences using value functions a general definition of the reper functions is given and discussed its properties; the notions of a reper utility function and a reper harm function, representing respectively the binary relations of utility and binary relations of harm on the set of vector estimates and on the set of objects, are considered;
- the formulation of the sensitivity analysis problem of multicriteria choice to a change in the estimates of the parametric importance of criteria is proposed; the general method of carrying out such an analysis for separate non-dominated alternatives and for sets of alternatives is given;
- within the framework of a comparative study of choice functions that depend on collective preferences, the study of collective choice functions based on the principle of stability was carried out; some properties and their set-theoretic relations are obtained for these solutions; some properties of procedures for constructing of aggregated rankings, based on the considered rules, are proven;
- within the framework of the preference diversity estimation a preference diversity and a preference polarization indices has been studied; new axiomatic properties of these indices have been developed; new preference diversity and preference polarization indices has been investigated and axiomatic justifications of the proposed indices has been obtained;
- within the framework of the study of coalitional manipulation under incomplete information it is shown that: a) for scoring rules the probability of coalitional manipulation is equal to the probability of individual manipulation when voters know winners of the election; b) coalitional manipulation under incomplete information is always safe for plurality rule and veto rule, however, it is not always safe for Borda rule; computational experiments are held for calculating the probability of coalitional manipulation under incomplete information;
- the risk weight multiplier correcting Basel requirements to cover risks arising from portfolio concentration and correlation of probability of default (PD) and the share of default losses (Loss Given Default-LGD) is calculated;
- the model for estimating the probability of default is constructed for shipping companies using the method of binary and categorical logistic regression on a sample of 192 shipping companies of 36 countries for the period from 2001 to 2016;
- the models for prediction of crises in the stock exchange based on the Hawkes processes has been developed; the models were tested on the S&P500 stock index data and the USD/RUB currency pair data;
- the aggregation of the recommendations of financial analysts within the framework of belief functions theory was studied on the example of the Russian stock market; it is shown that the aggregated forecasts obtained in most cases turn out to be more accurate than consensus forecasts;
- within the framework of the study of international migration a network model of international migration was developed and a centrality measures were calculated for the model; a relation between total number of migrants and socio-economic indicators of countries (GDP, educational level, intensity of conflicts) was analyzed;
- new models of conflict zones allocation were proposed and applied to the Arctic region; an analysis of conflict zones in the Barents Sea based on the level of interest in natural resources was performed;
- in the field of oil spills in the event of emergencies existing mathematical models of oil spills were studied; a dynamic model of oil spills was constructed; a software that allows to visualize the process of oil spills propagation was developed;
- in the field of food security international trade networks of products were analyzed; there were detected key participants of networks based on LRIC indices; changes of key participants that influence food security of other countries was analyzed over the time;
- on the basis of previously developed methods of pattern-clustering, numerical methods for calculating indices of heterogeneity of innovative development using the Global Innovation Index data are developed;
- in the development of methods for analysis of structural complexity, new modifications of the algorithm for analysis of the structural complexity of the graph, based on the normalized value of entropy, are considered and investigated; this modification allowed to accelerate and increase the accuracy of calculating the complexity of the stock market data in the problem of forecasting crisis periods;
- approaches to the operationalization of polarity in international researches have been studied and the relationship between the polarity and the likelihood of conflicts has been studied.
Level of implementation, recommendations on implementation or outcomes of the implementation of the results
Both fundamental and applied results have been obtained. Most applicable results have an analytical and a recommendation character.
