Modeling Risk Factors Interaction and Risk Estimation with Copulas

Abstract

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.