Research Information System
Thesis Type: Doctorate
Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey
Approval Date: 2019
Student: KÜBRA DURUKAN
Supervisor: HACI HASAN ÖRKCÜ
Open Archive Collection: AVESIS Open Access Collection
Abstract:Copula functions, which play an important role in insurance, actuarial and risk areas, are frequently used to explain the dependency structure of random variables. On the other hand, the risk aversion measure, which is defined based on utility functions, is an important decision-making tool used in the calculation of risk premium for insurance companies. In this study, the risk aversion matrix and risk premium vector for dependent bivariate risks are obtained by using the utility copula function given in Kettler (2007). The values of the risk premium vector are calculated for independent, semi-dependent and fully dependent risks. The risk aversion matrix and the risk premium vector are calculated for the different values of the copula dependency parameter and the results are presented in tables and graphs. In the continuation of the study, using the truncated distribution method, a new Sklar copula function is obtained for the utility copula given in Kettler (2007), which provides Sklar copula properties. At the end of the study, a simulation study is performed for this new copula. In this simulation study, the maximum likelihood estimation method is used to estimate the dependency parameter and it is shown that more accurate estimates are made for large samples. Using simulation data obtained for a selected parameter value, risk aversion coefficients and risk premium vectors are numerically calculated and the results are presented in tables and graphs. In addition, it is shown by numerical examples that an insurance company working with dependent risks should receive more premiums if it is risk aversion and less premiums if it is risk seeking.