Modelling dependency between different lines of business with copulas

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Jackie Li, Australia
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Summary:
This paper summarises some fundamental theories of copulas and investigates their practical use to model the underlying dependency structures between general insurance liabilities of different lines of business. The copulas under discussion include Gaussian copula, t copula, Cook-Johnson copula, and Archimedean copulas. Relevant Australian legislation and preliminary information are introduced in Sections 1 and 2. The general definition of a copula is set out in Section 3. Different types of copula and simulation techniques, with some examples for illustration, are introduced in Section 4. Examples of practical applications on assessing the uncertainty of some general insurance liabilities are provided in Sections 5 and 6. The conclusions are presented in Section 7. All the calculations were carried out through Excel spreadsheets with VBA (Visual Basic for Applications) coding and the software Mathematica. Details regarding the use of Excel functions and Mathematica coding can be provided upon request to the author. This paper is an excerpt of the author’s PhD thesis.
 
Date: 29 May - Time: 16:30 to 18:00 - Room: 253
Theme: 1.A. Stochastic dependence