publication . Article . 2012

Reversible Jump Markov Chain Monte Carlo Method for Parameter Reduction in Claims Reserving

Verrall, R. J.; Wüthrich, M. V.;
Open Access
  • Published: 26 Nov 2012 Journal: North American Actuarial Journal, volume 16, pages 240-259 (issn: 1092-0277, eissn: 2325-0453, Copyright policy)
  • Publisher: Informa UK Limited
  • Country: United Kingdom
We present an application of the reversible jump Markov chain Monte Carlo (RJMCMC) method to the important problem of setting claims reserves in general insurance business for the outstanding loss liabilities. A measure of the uncertainty in these claims reserves estimates is also needed for solvency purposes. The RJMCMC method described in this paper represents an improvement over the manual processes often employed in practice. In particular, our RJMCMC method describes parameter reduction and tail factor estimation in the claims reserving process, and, moreover, it provides the full predictive distribution of the outstanding loss liabilities.
free text keywords: Statistics, Probability and Uncertainty, Economics and Econometrics, Statistics and Probability, General insurance, Solvency, Economics, Econometrics, Parameter reduction, Reversible-jump Markov chain Monte Carlo, HG
16 references, page 1 of 2

[1] Bjorkwall, S., Hossjer, O.,Ohlsson, E., Verrall, R.J. (2010). A generalized linear model with smoothing e ects for claims reserving. Preprint.

[2] Buhlmann, H., De Felice, M., Gisler, A., Moriconi, F., Wuthrich, M.V. (2009). Recursive credibility formula for chain ladder factors and the claims development result. Astin Bulletin 39/1, 275-306.

[3] De Jong, P., Zehnwirth, B. (1983). Claims reserving, state-space models and the Kalman lter. J. Institute Actuaries 110, 157-182.

[4] England, P.D., Verrall, R.J. (2001). A exible framework for stochastic claims reserving. Proc. CAS 88, 1-38.

[5] England, P.D., Verrall, R.J. (2002). Stochastic claims reserving in general insurance. British Actuarial J. 8/3, 443-518.

[6] England, P.D., Verrall, R.J., Wuthrich, M.V. (2010). Bayesian overdispersed Poisson model and the Bornhuetter-Ferguson claims reserving method. Preprint.

[7] Gilks, W.R., Richardson, S., Spiegelhalter, D.J. (1996). Markov Chain Monte Carlo in Practice. Chapman & Hall.

[8] Gisler, A., Wuthrich, M.V. (2008). Credibility for the chain ladder reserving method. Astin Bulletin 38/2, 565-600.

[9] Green, P.J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82/4, 711-732.

[10] Green, P.J. (2003). Trans-dimensional Markov chain Monte Carlo. In: Highly Structured Stochastic Systems, P.J. Green, N.L. Hjort, S. Richardson (eds.), Oxford Statistical Science Series, 179-206. Oxford University Press.

[11] Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109.

[12] Johansen, A.M., Evers, L., Whiteley, N. (2010). Monte Carlo Methods. Lecture notes, Department of Mathematics, University of Bristol.

[13] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys. 21/6, 1087-1092. [OpenAIRE]

[14] Renshaw, A.E., Verrall, R.J. (1998). A stochastic model underlying the chain-ladder technique. British Actuarial J. 4/4, 903-923. [OpenAIRE]

[15] Verrall, R.J., Hossjer, O., Bjorkwall, S. (2010). Modelling claims run-o with reversible jump Markov chain Monte Carlo Methods. Preprint.

16 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue