The effects of parameter uncertainty in dependency structures

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Jakub M. Borowicz~James P. Norman, United-Kingdom
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Summary:
In this paper we analyse the effects of parameter uncertainty in dependency structures. Two copulas are analysed: the bivariate Gaussian copula and the Gumbel copula. We incorporate parameter uncertainty using Bayesian methods, for which we make use of Markov Chain Monte Carlo techniques. This approach is demonstrated with an example of a bivariate dataset representing average cost per claim for two lines of business. The effect of parameter uncertainty on the predictive copula distribution for both copulas is investigated. We find that the overall rank correlation of the Gaussian copula is reduced when considering parameter uncertainty, but that rank correlation of the upper tail is increased. Conversely, the overall rank correlation of the Gumbel copula is increased with the inclusion of parameter uncertainty, and the tail-correlation reduced. The approach we demonstrate can easily be incorporated in a Dynamic Financial Analysis (DFA) model.
 
Date: 1 June - Time: 11:00 to 12:30 - Room: 251
Theme: 1.A. Stochastic dependence