Economics - Research Publications
Permanent URI for this collection
Search Results
1 - 3 of 3
-
ItemApplication of Bayesian models with Markov chain Monte Carlo simulation to real claims data( 2006-08)In this paper we demonstrate an application of Bayesian models with Markov chain Monte Carlo (MCMC) simulation to some real claims data (gross of reinsurance) of three Australian private lines of business via the use of BUGS (Bayesian Inference Using Gibbs Sampling). We take the accident period effect and the development period effect into account and consider parameter error and process error. We devise an approximation for the over-dispersed Poisson (ODP) assumption in BUGS and select suitable non-informative priors. We also make use of some formal model criticism procedures to validate the selected model structures. We then compare our estimates with the actual claim payments made after the valuation date. We find that BUGS generally provides parameter estimates consistent with those produced by generalised linear models (GLMs). Moreover, our estimates of the expected total outstanding claims liability plus the aggregate risk margin cover the actual claim payments appropriately.
-
ItemModelling dependency betweeen different lines of business with copulas( 2006-08)In this paper we select various practically tractable copulas and demonstrate their use in practical circumstances under the current Australian regulatory framework. The copulas under discussion include Gaussian copula, t copula, Cook-Johnson copula, and a fewArchimedean copulas. We also examine the feasibility of the simulation procedures of the copulas in practice. We set up two hypothetical examples, which are based on real lifeclaims features. In particular, we propose the incorporation of a copula into the traditionalcollective risk model. We demonstrate that copulas are a set of flexible mathematical tools for modelling dependency, in which the extreme percentiles of the aggregate portfolio value vary considerably for different choices of model copulas. We also showthat some measures of association have better properties than the correlation coefficient, which is a common measure in practice.Relevant legislation and preliminary information are introduced in Sections 1 and 2. The general definition of a copula is set out in Section 3. Some elementary measures ofassociation between pairwise random variables, for computing the parameters of the copulas, are described in Section 4. Different types of copula and simulation techniques, with some examples for illustration, are introduced in Section 5. Examples of practicalapplications on assessing the uncertainty of some general insurance liabilities are provided in Sections 6 and 7. Final discussion is set forth in Section 8.
-
ItemComparison of stochastic reserving methods( 2006-01)This paper compares several stochastic reserving methods on both qualitative and quantitative aspects in dealing with the outstanding claims liabilities. These methods include Bayesian estimation with Markov chain Monte Carlo (MCMC) simulation, the chain ladder method with bootstrapping, generalised linear models (GLMs) with bootstrapping, the Kalman filter on state-space models, the Mack model, and the stochastic chain ladder method. To start with, the outline of this paper and different types of uncertainty are set forth in Sections 1 and 2. The notation and terminology are stated in Section 3. The strengths and limitations of the methods are examined by considering the underlying structures, assumptions, and estimation mechanics, in Sections 4 to 10. The application of each method is then tested on a particular claims data set in Section 11, similar to the analysis in Mack (1993a). Conclusions are presented in Section 12. This paper is an excerpt of the author’s PhD thesis.All the calculations were done on Excel spreadsheets with VBA (Visual Basic for Applications) coding and the software BUGS (Bayesian Inference Using Gibbs Sampling). When large amounts of simulation were carried out in the analysis, approximation formulae were used to provide reasonable checks. In addition, some proofs and derivations are stated in the appendices for reference purposes. Details regarding the use of VBA and BUGS codings can be provided upon request to the author.