MODELING RISK FACTORS INTERACTION AND RISK ESTIMATION WITH COPULAS
Keywords:multivariate stochastic processes, risk estimation, special copula functions, modeling multivariate distributions, combined marginal distributions
Context. Various risks are inherent to practically all types of human activities. Usually the risks are characterized by availability of multiple risk factors, uncertainties, incompleteness and low quality of data available. The problem of mathematical modeling of risks is very popular with taking into consideration possible uncertainties and interaction of risk factors. Such models are required for solving the problems of loss forecasting and making appropriate managerial decisions.
Objective. The purpose of the study is in development of multivariate risk modeling method using specialized copula functions.The models are developed in the form of multivariate distributions.
Method. The modeling methodology is based upon exploring the special features of various copula functions that are helpful to construct appropriate multivariate distributions for the risk factors selected. The study contains formal description of selected copulas, analysis of their specific features and possibilities for practical applications in the risk management area. Examples of practical applications of the copula based approach to constructing multivariate distributions using generated and actual statistical data are provided.
Results. The results achieved will be useful for further theoretical studies as well as for practical applications in the area of risk management. The distributions constructed with copula create a ground for solving the problems of forecasting possible loss and making appropriate decision regarding risk management.
Conclusions. Thus the problem of constructing multivariate distributions for multiple risk factors can be solved successfully using special copula functions.
Nystrom K., Skoglund J. Univariate Extreme Value Theory, GARCH and Measures of Risk, Stockholm: Swedbank, Group of Financial Risk Control, 2002, Vol. 11, pp. 1–27.
Bhatti M. I., Hung Quang Do Recent Developments in Copula and Its Applications to the energy, Forestry and Environmental Sciences, International Journal of Hydrogen Energy, 2019. Vol. 44, Number 36, pp. 19453–19473.
Kluppelberg C. Risk Management with Extreme Value Theory. New York, Chapman & Hall, 2003, 405 p.
Bassi F., Embrechts P., Kafetzaki M. Risk management and quantile estimation, A Practical Guide to Heavy Tails; Ed. R.J. Adler. Boston, Birkhauser, 1998, Vol. 4, pp. 111–130.
Embrechts P. Eds.: B. Finkenstadt, H. Rootzen. Extremes in Economics and the Economics of Extremes, 2001, Vol. 12. pp. 169–183.
Embrechts P., Haan L., Huang X. Modelling multivariate extremes, RISK Books, 2000, Vol. 12, pp. 59–67.
Bouye E. Multivariate extremes at work for portfolio risk measurement, Finance: Presses universitaires de France, 2002, Vol. 23, Nubmer 2, pp. 125–144.
Rootzen H., Tajvidi N. The multivariate generalized Pareto distribution, Bernoulli, 2006, Vol. 12, pp. 917–930.
Bidyuk P. І., Kroptya A. V. Analysis and methods of solving the problem of extreme values estimation, Scientific Bulletin of NTUU KPI, 2005, No. 4, pp. 34–47.
Blum P., Dias A., Embrechts P. The ART of dependence modelling: the latest advances in correlation analysis, Alternative Risk Strategies: RISK Books, 2002, Vol. 7, pp. 339–356.
Embrechts P., McNeil A. J., Straumann D. Correlation: Pitfalls and alternatives, Risk, 1999, Vol. 12, pp. 69–71.
Embrechts P., McNeil A. J., Straumann D. Correlation and dependence in risk management. Cambridge, Cambridge University Press, 2002, pp. 176–223.
Edward W., Valdez E. Understanding relationships using copulas, North American Actuarial Journal, 1998, Vol. 2. Number 1, pp. 1–25.
Nelsen R. B. An Introduction to Copulas. New York, Springer, 2006, 270 p.
Newey W. K., McFadden D. Large Sample Estimation and Hypothesis Testing, Handbook of Econometrics, 1994, Vol. 4, pp. 2111–2245.
Вashkov E., Dmitrieva O., Huskova N. et al. Parallel multiple blocked methods of Bickart type, Proceedings of SPIE – The International Society for Optical Engineering, 2019, No. 11176, P. 9.
Miroshkin O., Kovalov S., Dmitrieva O. et al. ParSimTech Research and Training Center, IEEE European Technology and Engineering Management Summit (E-TEMS), 2020, pp. 1–4.
Siddhartha M. Gold Price Prediction Dataset [E’lektronnyj resurs]. Rezhim dostupa, https://www.kaggle.com/sid321axn/gold-price-predictiondataset
How to Cite
Copyright (c) 2022 Н. В. Кузнецова, В. Г. Гуськова, П. И. Бидюк, Й. Мацуки, Л. Б. Левенчук
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.