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Modelling Claims Run-Off with Reversible Jump Markov Chain Monte Carlo Methods

  • Richard Verrall (a1), Ola Hössjer (a2) and Susanna Björkwall (a2)

Abstract

In this paper we describe a new approach to modelling the development of claims run-off triangles. This method replaces the usual ad hoc practical process of extrapolating a development pattern to obtain tail factors with an objective procedure. An example is given, illustrating the results in a practical context, and the WinBUGS code is supplied.

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Björkwall, S., Hössjer, O., Ohlsson, E. and Verrall, R. (2011) A generalized linear model with smoothing effects for claims reserving. Insurance, Mathematics and Economics, 49, 2737.
Brooks, S. and Gelman, A. (1998) General Methods for Monitoring Convergence of Iterative Simulations. Journal of Computational and Graphical Statistics, 7(4), 434455.
Brooks, S.P. and Roberts, G.O. (1998) Convergence Assessment Techniques for Markov Chain Monte Carlo. Statistics and Computing, 8(4), 319335.
Congdon, P. (2006). Bayesian Statistical Modelling, John Wiley.
Cowles, M.K. and Carlin, B.P. (1996) Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review. Journal of the American Statistical Association, 91, 883904.
de Alba, E. (2002) Bayesian Estimation of Outstanding Claim Reserves. North American Actuarial Journal, 6, 120.
England, P.D. and Verrall, R.J. (2002) Stochastic Claims Reserving in General Insurance (with discussion). British Actuarial Journal, 8, 443544.
England, P.D. and Verrall, R.J. (2006) Predictive Distributions of Outstanding Liabilities in General Insurance. Annals of Actuarial Science, 1, 221270.
England, P.D., Wüthrich, M.V. and Verrall, R.J. (2010) Bayesian Overdispersed Poisson Model and the Bornhuetter-Ferguson Claims Reserving Method. Pre-print.
Fan, Y., Peters, G.W. and Sisson, S.A. (2009) Automating and evaluating reversible jump MCMC proposal. Statistics and Computing 19, 409421.
Geman, S. and Geman, D. (1984) Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721741.
Gelfand, A.E. and Smith, A.F.M. (1990) Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85, 398409.
Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. (1995) Bayesian Data Analysis. Chapman and Hall, London.
Gelman, A. and Rubin, D.B. (1992) Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 7, 457511.
Geweke, J. (1991) Evaluating the Accuracy of Sampling Based Approaches to the Calculation of Posterior Moments. Federal Reserve Bank of Minneapolis. Research Department Staff Report 148.
Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (1996) Markov Chain Monte Carlo in Practice. Chapman and Hall, London.
Green, P.J. (1995) Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika, 82, 711732.
Hoeting, J.A., Madigan, D., Raftery, A.E. and Volinsky, C.T. (1999) Bayesian Model Averaging: A Tutorial. Statistical Science, 14(4), 382417.
Katsis, A. and Ntzoufras, I. (2005) Testing Hypotheses for the Distribution of Insurance Claim Counts Using the Gibbs Sampler. Journal of Computational Methods in Sciences and Engineering, 5, 201214.
Lunn, D.J., Best, N. and Whittaker, J.C. (2009) Generic Reversible Jump MCMC Using Graphical Models. Statistics and Computing, 19, 395408.
Lunn, D.J., Thomas, A., Best, N. and Spiegelhalter, D. (2000) WinBUGS — a Bayesian Modelling Framework: Concepts, Structure, and Extensibility. Statistics and Computing, 10, 325337.
Makov, U. (2001) Principal Applications of Bayesian Methods in Actuarial Science: A Perspective. North American Actuarial Journal, 5, 5360.
Nevat, I., Peters, G.W. and Yuan, J. (2009) Channel Estimation in OFDM Systems with Unknown Power Delay Profile Using Transdimensional MCMC via Stochastic Approximation. 69th Vehicular Technology Conference, VTC, Spring 2009, 16.
Ntzoufras, I. (2009) Bayesian Modeling Using WinBUGS, John Wiley.
Ntzoufras, I. and Dellaportas, P. (2002) Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty (with discussion). North American Actuarial Journal, 6, 113128.
Ntzoufras, I., Katsis, A. and Karlis, D. (2005) Bayesian Assessment of the Distribution of Insurance Claim Counts Using Reversible Jump MCMC. North American Actuarial Journal, 9, 90108.
Peters, G.W., Shevchenko, M.V. and Wüthrich, P.V. (2009) Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models. Astin Bulletin, 39(1), 133.
Renshaw, A.E. and Verrall, R.J. (1998) A Stochastic Model Underlying the Chain Ladder Technique. British Actuarial Journal, 4 (IV), 903923.
Roberts, G.O. and Rosenthal, J.S. (2007) Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms. Journal of Applied Probability, 44(2), 458475.
Roberts, G.O. and Rosenthal, J.S. (2009) Examples of Adaptive MCMC. Journal of Computational and Graphical Statistics, 18(2), 349367.
Scollnik, D.P.M. (2001) Actuarial Modelling with MCMC and BUGS. North American Actuarial Journal, 5(2), 96125.
Scollnik, D.P.M. (2002) Implementation of Four Models for Outstanding Liabilities in WinBUGS: A discussion of a paper by Ntzoufras and Dellaportas, North American Actuarial Journal, 6, 128136.
Sisson, S.A. (2005) Transdimensional Markov Chains. Journal of the American Statistical Association, 100(471), 10771089.
Smith, B.J. (2007) boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference. Journal of Statistical Software, 21(11), 137.
Taylor, G.C. and Ashe, F.R. (1983) Second Moments of Estimates of Outstanding Claims. Journal of Econometrics, 23, 3761.
Verrall, R.J. (2007) Obtaining Predictive Distributions for Reserves Which Incorporate Expert Opinion. Variance (Casualty Actuarial Society Journal), 1, 5380.
Verrall, R.J. and Wüthrich, M.V. (2010) Reversible Jump Markov Chain Monte Carlo Method for Parameter Reduction in Claims Reserving.
Wüthrich, M.V. (2007) Using a Bayesian Approach for Claims Reserving. Variance, 1(2), 292301.
Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving in Insurance. John Wiley.

Modelling Claims Run-Off with Reversible Jump Markov Chain Monte Carlo Methods

  • Richard Verrall (a1), Ola Hössjer (a2) and Susanna Björkwall (a2)

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