Stochastic Claims Reserving in General Insurance

ABSTRACT This paper considers a wide range of stochastic reserving models for use in general insurance, beginning with stochastic models which reproduce the traditional chain-ladder reserve estimates. The models are extended to consider parametric curves and smoothing models for the shape of the development run-off, which allow extrapolation for the estimation of tail factors. The Bornhuetter-Ferguson technique is also considered, within a Bayesian framework, which allows expert opinion to be used to provide prior estimates of ultimate claims. The primary advantage of stochastic reserving models is the availability of measures of precision of reserve estimates, and in this respect, attention is focused on the root mean squared error of prediction (prediction error). Of greater interest is a full predictive distribution of possible reserve outcomes, and different methods of obtaining that distribution are described. The techniques are illustrated with examples throughout, and the wider issues discussed, in particular, the concept of a ‘best estimate’; reporting the variability of claims reserves; and use in dynamic financial analysis models.

[1]  Richard Verrall,et al.  A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving , 2004 .

[2]  P. D. England,et al.  Addendum to “Analytic and bootstrap estimates of prediction errors in claims reserving” , 2002 .

[3]  David P. M. Scollnik,et al.  Actuarial Modeling with MCMC and BUGs , 2001 .

[4]  T. Mack.  Credible Claims Reserves: the Benktander Method , 2000, ASTIN Bulletin.

[5]  G. Taylor,et al.  Loss Reserving: An Actuarial Perspective , 2000 .

[6]  G. Venter,et al.  A comparison of stochastic models that reproduce chain ladder reserve estimates , 2000 .

[7]  Richard Verrall,et al.  An investigation into stochastic claims reserving models and the chain-ladder technique , 2000 .

[8]  P. England,et al.  Comments on: "A comparison of stochastic models that reproduce chain ladder reserve estimates", by Mack and Venter , 2000 .

[9]  P. England,et al.  Analytic and bootstrap estimates of prediction errors in claims reserving , 1999 .

[10]  R. Norberg.  Prediction of Outstanding Liabilities II. Model Variations and Extensions , 1999, ASTIN Bulletin.

[11]  Thomas h ack.  Measuring the Variability of Chain Ladder Reserve Estimates , 1999 .

[12]  Unbiased Loss Development Factors , 1999 .

[13]  Richard Verrall,et al.  A Stochastic Model Underlying the Chain-Ladder Technique , 1998, British Actuarial Journal.

[14]  Glen Barnett,et al.  2000 BEST ESTIMATES FOR RESERVES , 1998 .

[15]  R. Verrall.  Claims reserving and generalised additive models , 1996 .

[16]  B. Ripley,et al.  Modern Applied Statistics with S-Plus. , 1996 .

[17]  Klaus D. Schmidt,et al.  An Extension of Mack's Model for the Chain Ladder Method , 1996, ASTIN Bulletin.

[18]  E. Arjas,et al.  Claims Reserving in Continuous Time; A Nonparametric Bayesian Approach , 1996, ASTIN Bulletin.

[19]  L. Doray.  UMVUE of the IBNR reserve in a lognormal linear regression model , 1996 .

[20]  A. E. Renshaw.  Claims reserving by joint modelling. , 1996 .

[21]  Shaun S. Wang,et al.  Insurance pricing and increased limits ratemaking by proportional hazards transforms , 1995 .

[22]  R. Tibshirani,et al.  Generalized additive models for medical research , 1995, Statistical methods in medical research.

[23]  T. Mack.  Which stochastic model is underlying the chain ladder method , 1994 .

[24]  David A. James.  Modern Applied Statistics With S-PLUS , 1994 .

[25]  R. Verrall.  A Method for Modelling Varying Run-Off Evolutions in Claims Reserving , 1994 .

[26]  B. Silverman,et al.  Nonparametric regression and generalized linear models , 1994 .

[27]  T. Mack.  Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates , 1993, ASTIN Bulletin.

[28]  Ragnar Norberg,et al.  Prediction of Outstanding Liabilities in Non-Life Insurance , 1993, ASTIN Bulletin.

[29]  Thomas Mack,et al.  A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves , 1991, ASTIN Bulletin.

[30]  Richard Verrall,et al.  On the estimation of reserves from loglinear models , 1991 .

[31]  C. Ramsay.  On blocked poisson processes in risk theory , 1991 .

[32]  T. Hastie,et al.  Statistical Models in S , 1991 .

[33]  R. Verrall,et al.  Chain ladder and maximum likelihood , 1991 .

[34]  T. S. Wright.  A stochastic method for claims reserving in general insurance , 1990 .

[35]  Richard Verrall,et al.  Bayes and Empirical Bayes Estimation for the Chain Ladder Model , 1990, ASTIN Bulletin.

[36]  A. Renshaw.  Chain ladder and interactive modelling. (Claims reserving and GLIM) , 1989 .

[37]  R. Verrall.  A STATE SPACE REPRESENTATION OF THE CHAIN LADDER LINEAR MODEL , 1989 .

[38]  Greg Taylor,et al.  Second moments of estimates of outstanding claims , 1983 .

[39]  Ben Zehnwirth,et al.  Claims reserving, state-space models and the Kalman filter , 1983 .

[40]  Erhard Kremer,et al.  IBNR-claims and the two-way model of ANOVA , 1982 .

[41]  Edmund Taylor Whittaker.  On a New Method of Graduation , 1922, Proceedings of the Edinburgh Mathematical Society.