Spatial modelling of claim frequency and claim size in non-life insurance

Scandinavian Actuarial Journal

Volumn 2007, Issue 3, 2007, Pages 202-225

  Gschlößl, Susanne ^a   Czado, Claudia ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Bayesian inference; Compound poisson model; Non life insurance; Proper scoring rules; Spatial regression models

Indexed keywords

EID: 42749097176     PISSN: 03461238     EISSN: 16512030     Source Type: Journal    
DOI: 10.1080/03461230701414764     Document Type: Article

References (29)

1. Besag, J. & Kooperberg, C. (1995). On conditional and intrinsic autoregressions. Biometrika 82, 733-746.
2. Besag, J., York, J. & Mollié, A. (1991). Bayesian image restoration with two applications in spatial statistics. Annals of the Institute of Statistics and Mathematics 43, 1-59 (with discussion).
3. Boskov, M. & Verrall, R. (1994). Premium rating by geographic area using spatial models. Astin Bulletin 24 (1), 131-143.
4. Consul, P. & Jain, G. (1973). A generalization of the Poisson distribution. Technometrics 15, 791-799.
5. Czado, C. & Prokopenko, S. (2004). Modeling transport mode decisions using hierarchical binary spatial regression models with cluster effects. Discussion paper 406, SFB 386 Statistische Analyse diskreter Strukturen. http://www.stat.uni-muenchen.de/sfb386/.
6. Dimakos, X. & Frigessi, A. (2002). Bayesian premium rating with latent structure. Scandinavian Actuarial Journal 2002 (3), 162-184.
7. Gelfand, A. & Ghosh, S. (1998). Model choice: a minimum posterior predictive loss approach. Biometrika 85 (1), 1-11.
8. Gilks, W., Richardson, S. & Spiegelhalter, D. (1996). Markov Chain Monte Carlo in practice. Boca Raton: Chapman & Hall/CRC.
9. Gneiting, T. & Raftery, A. E. (2007). Strictly proper scoring rules, prediction and estimation. Journal of the American Statistical Association 102 (477), 359-378.
10. Gschlößl, S. (2006). Hierarchical Bayesian spatial regression models with applications to nonlife insurance. Ph. D. thesis. Munich University of Technology.
11. Gschlößl, S. & Czado, C. (2005). Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler? Discussion paper 460, SFB 386 Statistische Analyse diskreter Strukturen, http://www.stat.uni-muenchen.de/sfb386
12. Gschlößl, S. & Czado, C. (2006). Modelling count data with overdispersion and spatial effects. Statistical Papers (Online first). http://www.springerlink.com/content/1134645365u34r2n
13. Haberman, S. & Renshaw, A. (1996). Generalized linear models and actuarial science. The Statistician 45, 407-436.
14. Han, C. & Carlin, B. (2001). Markov Chain Monte Carlo methods for computing Bayes factors: a comparative review. Journal of the American Statistical Association 96, 1122-1132.
15. Jørgensen, B. & de Souza, M. C. P. (1994). Fitting Tweedie’s compound Poisson model to insurance claims data. Scandinavian Actuarial Journal 1, 69-93.
16. Kass, R. & Raftery, A. (1995). Bayes factors and model uncertainty. Journal of the American Statistical Association 90, 773-795.
17. Laud, P. & Ibrahim, J. (1995). Predictive model selection. Journal of the Royal Statistical Society. Series B. Statistical Methodology 57 (1), 247-262.
18. Lundberg, F. (1903). Approximerad framställning av sannolikhetsfunktionen. aterförsäkring av kollektivrisker. Akad. afhandling. almqvist och wicksell, Uppsala, Almqvist ochWicksell, Uppsala.
19. Mikosch, T. (2004). Non-life insurance mathematics. an introduction with stochastic processes. New York: Springer.
20. Panjer, H. (1981). Recursive evaluation of a family of compound distributions. Astin Bulletin 11, 22-26.
21. Panjer, H. & Willmot, G. (1983). Compound Poisson models in actuarial risk theory. Journal of Econometrics 23, 63-76.
22. Pettitt, A., Weir, I. & Hart, A. (2002). A conditional autoregressive Gaussian process for irregularly spaced multivariate data with application to modelling large sets of binary data. Statistics and Computing 12 (4), 353-367.
23. Renshaw, A. (1994). Modelling the claims process in the presence of covariates. Astin Bulletin 24, 265-285.
24. Smyth, G. K. & Jørgensen, B. (2002). Fitting Tweedie’s compound Poisson model to insurance claims data: dispersion modelling. Astin Bulletin 32 (1), 143-157.
25. Spiegelhalter, D., Best, N., Carlin, B. & van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of Royal Statistics Society B 64 (4), 583-640.
26. Sun, D., Tsutakawa, R. K. & Speckman, P. L. (1999). Posterior distribution of hierarchical models using CAR(1) distributions. Biometrika 86, 341-350.
27. Székely, G. (2003). O-Statistics: the energy of statistical samples. Technical report no. 2003-16, Department of Mathematics and Statistics, Bowling Green State University, Ohio.
28. Taylor, G. (1989). Use of spline functions for premium rating by geographic area. Astin Bulletin 19 (1), 89-122.
29. van der Linde, A. (2005). DIC in variable selection. Statistica Neerlandica 59 (1), 45-56.