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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">umovest</journal-id><journal-title-group><journal-title xml:lang="ru">Статистика и Экономика</journal-title><trans-title-group xml:lang="en"><trans-title>Statistics and Economics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2500-3925</issn><publisher><publisher-name>Plekhanov Russian University of Economics</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21686/2500-3925-2025-4-36-51</article-id><article-id custom-type="elpub" pub-id-type="custom">umovest-1903</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>СТАТИСТИКА И МАТЕМАТИЧЕСКИЕ МЕТОДЫ В ЭКОНОМИКЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>STATISTICAL AND MATHEMATICAL METHODS  IN ECONOMICS</subject></subj-group></article-categories><title-group><article-title>Экономико-математическое моделирование рисков в сервисной бизнес-модели сетевого предприятия</article-title><trans-title-group xml:lang="en"><trans-title>Economic and Mathematical Modeling of Risks in the Service Business Model of a Network Enterprise</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Брызгалов</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Bryzgalov</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Алексеевич Брызгалов, ассистент кафедры прикладной информатики и информационной безопасности</p><p>Москва</p></bio><bio xml:lang="en"><p>Alexey Alekseevich Bryzgalov, Assistant of the Department of Applied Informatics and Information Security</p><p>Moscow</p></bio><email xlink:type="simple">Bryzgalov.AA@rea.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Российский экономический университет им. Г.В. Плеханова</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Plekhanov Russian University of Economics</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>29</day><month>08</month><year>2025</year></pub-date><volume>22</volume><issue>4</issue><fpage>36</fpage><lpage>51</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Брызгалов А.А., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Брызгалов А.А.</copyright-holder><copyright-holder xml:lang="en">Bryzgalov A.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://statecon.rea.ru/jour/article/view/1903">https://statecon.rea.ru/jour/article/view/1903</self-uri><abstract><p>Целью работы является разработка экономико-математической модели оценки рисков в сервисной бизнес-модели сетевого предприятия, способной формализовать влияние разнообразных факторов риска на устойчивость сетевой структуры и вырабатывать эффективные стратегии управления ими.</p><sec><title>Материалы и методы</title><p>Материалы и методы. В работе применены стохастические методы, методы оптимизации, теория графов, системная динамика. Алгоритм моделирования включает этапы идентификации рисков, формализации параметров, анализа каскадных эффектов, оценки сетевой структуры и оптимизации стратегии управления. В качестве эмпирической базы использован пример IoT-платформы MindSphere и экосистемы её участников.</p></sec><sec><title>Результаты</title><p>Результаты. Разработан комплексный подход к количественной оценке рисков в цифровых экосистемах на основе каскадного анализа, оценки центральности узлов экосистемы и моделирования ущерба. Комплексный подход к количественной оценке рисков предусматривает интеграцию методов, позволяющих не только измерить вероятность и потенциальный ущерб отдельных угроз, но и учесть их взаимосвязи, динамику развития и влияние на структуру сервисной бизнес-модели сетевого предприятия. Такой подход обеспечивает не только расчет ожидаемых потерь, но и выявление критических точек системы, разработку превентивных мер и визуализацию результатов для принятия обоснованных решений, что особенно важно для сложной эко-системы, где риски усиливаются за счет взаимозависимости ее участников.</p></sec><sec><title>Заключение</title><p>Заключение. Разработанная модель позволяет количественно оценивать взаимосвязанные риски в сервисных бизнес-моделях, учитывать сетевую взаимосвязь рисков и структурные уязвимости экосистем. Это обеспечивает обоснованное принятие решений при управлении устойчивостью сетевой структуры. Результаты имеют практическое значение для промышленности, активно внедряющей IoT и облачные решения.</p></sec></abstract><trans-abstract xml:lang="en"><p>The aim of the research is to develop an economic and mathematical model of risk assessment in the service business model of a network enterprise, capable of formalizing the impact of various risk factors on the stability of the network structure and developing effective strategies for managing them.</p><sec><title>Materials and methods</title><p>Materials and methods. The paper uses stochastic methods, optimization methods, graph theory, and system dynamics. The modeling algorithm includes the stages of risk identification, parameter formalization, cascade effects analysis, network structure assessment, and management strategy optimization. The example of the MindSphere IoT-platform and the ecosystem of its participants is used as an empirical base.</p></sec><sec><title>Results</title><p>Results. A comprehensive approach to quantitative risk ssessment in digital ecosystems has been developed based on cascade analysis, assessment of the centrality of ecosystem nodes, and damage modeling. A comprehensive approach to quantitative risk assessment involves the integration of methods that allow not only to measure the probability and potential damage of individual threats, but also consider their interrelationships, development dynamics and impact on the structure of the service business model of a network enterprise. This approach provides not only the calculation of expected losses, but also the identification of critical points of the system, the development of preventive measures and visualization of the results for informed decision-making, which is especially important for a complex ecosystem where risks are increased due to the interdependence of its participants.</p></sec><sec><title>Conclusion</title><p>Conclusion. The developed model allows quantifying interrelated risks in service business models, taking into account the network interconnection of risks and structural vulnerabilities of ecosystems. This ensures informed decision-making when managing the stability of the network structure. The results are of practical importance for the industry, which is actively implementing IoT and cloud solutions</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>экономико-математическое моделирование</kwd><kwd>сервисные бизнес-модели</kwd><kwd>сетевые предприятия</kwd><kwd>управление&#13;
рисками</kwd><kwd>каскадные эффекты</kwd><kwd>системная динамика</kwd><kwd>теория&#13;
графов</kwd><kwd>центральность узлов</kwd><kwd>метод Монте-Карло</kwd><kwd>стохастическая оптимизация</kwd><kwd>устойчивость сети</kwd><kwd>цифровая экосистема</kwd><kwd>IoT-платформы</kwd></kwd-group><kwd-group xml:lang="en"><kwd>economic and mathematical modeling</kwd><kwd>service business models</kwd><kwd>network enterprises</kwd><kwd>risk management</kwd><kwd>cascading effects</kwd><kwd>system dynamics</kwd><kwd>graph theory</kwd><kwd>node centrality</kwd><kwd>Monte Carlo method</kwd><kwd>stochastic optimization</kwd><kwd>network stability</kwd><kwd>digital ecosystem</kwd><kwd>IoT platforms</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Fliaster A., Dellermann D. The risks of digital innovation: An ecosystem perspective [Электрон. ресурс] // Organizing for Digital Innovation. 2016. С. 1–22. 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