A Comparison of Stochastic Claims Reserving Methods

A Comparison of Stochastic Claims Reserving Methods



Abstract Views
536

Downloads
468

Citations

Share

##plugins.themes.bootstrap3.article.sidebar##

Table of Contents

##plugins.themes.bootstrap3.article.main##

In order to preserve their solvency, it is very important for insurance companies to accurately estimate their future required reserves. The aim of this article is to determine reserves by using different stochastic models: 1) distribution-free model (Mack's model), 2) probability distribution based models (Normal, Poisson, Gamma and Inverse Gaussian distributions), and 3) these latter probability based models combined with bootstrapping. To implement these models we used data on life-insurance and non-life insurance. Our findings indicate among distribution based methods, Mack's model (dataset 1 and 2) and Gamma probability distribution based model (dataset 3) are the best model in estimating reserves. The model based on Normal distribution produces the worst results, whatever the dataset. Regarding results of bootstrapping based on probability distribution models, they show that method based on Normal probability distribution (dataset 1 and 3) and ODP distribution (dataset 2) fit better. Our results also indicate that bootstrap method based on Chain-Ladder performs quit similarly than the best fitting probability distribution based bootstrap models. Among all retained models, methods based on bootstrapping present higher good-of-fit.

Keywords: Technical Provision, Chain Ladder, Stochastic Models, Bootstrapping.
  1. T. Mack. Distribution-free calculation of the standard error of chain-ladder reserve estimates. ASTIN Bulletin, 23:213–225, 1993.  |   Google Scholar
  2. E. Kremer. Ibnr claims and the two way model of anova.  |   Google Scholar
  3. Scandinavian Actuarial Journal, pages 47–55, 1982.  |   Google Scholar
  4. G.C. Taylor and F.R. Ashe. Second moments of estimates  |   Google Scholar
  5. of outstanding claims. Journal of Econometrics, 23(1):  |   Google Scholar
  6. B. Zehnwirth. Interactive claims reserving forecasting system. Insureware St.Kilda Australia, 1985.  |   Google Scholar
  7. A.E. Renshaw. Chain-ladder and interactive modelling (claims reserving and glim). Journal of the Institute of Actuaries, (116):559–587, 1989.  |   Google Scholar
  8. S. Christofides. Regression models based on logincremental payments. Claims Reserving Manual, Institute of Actuaries, London, 2, 1990.  |   Google Scholar
  9. R.J. Verrall. Bayes and empirical bayes estimation for the chain-ladder model. ASTIN Bulletin, 20(2):217–243, 1990.  |   Google Scholar
  10. R. Verrall. On the estimation of reserves from loglinear models. Insurance Mathematics and Economics, 10:75–80, 1991.  |   Google Scholar
  11. P. England and R. Verrall. Analytic and bootstrap estimates of prediction errors in claims reserving. Insurance: Mathematics and Economics, 25:281–293, 1999.  |   Google Scholar
  12. N. Kulikov and S. Dixon. Life insurance & wealth management practice committee. Discussion Note: IBNR, (December 2014), 2014.  |   Google Scholar
  13. P.D. England and R.J. Verrall. Stochastic claims reserving in general insurance. British Actuarial Journal, 8(3): 443–518, 2002.  |   Google Scholar
  14. R.J. Verrall. A state space representation of the chainladder linear model. Journal of the Institute of Actuaries, 116(7):589–610, 1989.  |   Google Scholar
  15. R.J. Verrall. On the unbiased estimation of reserves from loglinear models. Insurance: Mathematics and Economics, 10(1):75–80, 1991a.  |   Google Scholar
  16. R.J. Verrall. Chain-ladder and maximum likelihood. Journal of the Institute of Actuaries, 118:489–499, 1991b.  |   Google Scholar
  17. R.J. Verrall. A method for modelling varying run-off evolutions in claims reserving. ASTIN Bulletin, 24(2): 325–332, 1994.  |   Google Scholar
  18. R.J. Verrall. Claims reserving and generalised additive  |   Google Scholar
  19. models. Insurance: Mathematics and Economics, 19:31–43, 1996.  |   Google Scholar
  20. R.J. Verrall. An investigation into stochastic claims reserving models and the chain-ladder technique. Insurance: Mathematics and Economics, 26:91–99, 2000.  |   Google Scholar
  21. T. Mack. Which stochastic model is underlying the chainladder model? Insurance:Mathematics and Economics, (15):133–138, 1994a.  |   Google Scholar
  22. T. Mack. Measuring the variability of chain-ladder reserve estimates. Casualty Actuarial Society, Spring Forum, 1994b.  |   Google Scholar
  23. D.M. Murphy. Unbiased loss development factors. PCAS LXXXI, pages 154–222, 1994.  |   Google Scholar
  24. K.D. Schmidt and A. Schnaus. An extension of mack’s  |   Google Scholar
  25. model for the chain-ladder method. ASTIN Bulletin, 26: 247–262, 1996.  |   Google Scholar
  26. G. Barnett and B. Zehnwirth. Best estimates for reserves.  |   Google Scholar
  27. Casualty Actuarial Society,Fall Forum., 1998.  |   Google Scholar
  28. A.E. Renshaw and R.J. Verrall. A stochastic model underlying the chain-ladder technique. British Actuarial Journal, 4(4):903–923, 1998.  |   Google Scholar
  29. T. Mack and G. Venter. A comparison of stochastic models that reproduce chain-ladder reserve estimates. Insurance: Mathematics and Economics, 26:101–107, 2000.  |   Google Scholar
  30. P.D. England and R.J. Verrall. A flexible framework for  |   Google Scholar
  31. stochastic claims reserving. Casualty Actuarial Society, 2001.  |   Google Scholar
  32. M. Buchwalder, H. Bhlmann, M. Merz, and M. Wthrich.  |   Google Scholar
  33. The mean square error of prediction in the chain-ladder reserving method (mack and murphy revisited). ASTIN Bulletin, 36(2):521–542, 2006.  |   Google Scholar
  34. T. Mack, G. Quarg, and C. Braun. The mean square error of prediction in the chain-ladder reserving method - a comment. ASTIN Bulletin, 36(2):543–552, 2006.  |   Google Scholar
  35. M. Merz and M. V. Wthrich. Paid-incurred chain claims reserving method. Insurance: Mathematics and Economics, 46(3):568–579, 2010.  |   Google Scholar
  36. S. Hachemeister and Stanard. Ibnr claims count estimation with static lag functions. Spring Meeting of the Casualty Actuarial Society, 1975.  |   Google Scholar
  37. T. Mack. A simple parametric model for rating automobile insurance or estimating ibnr claims reserves. ASTIN Bulletin, 21:93–109, 1991.  |   Google Scholar
  38. A.E. Renshaw and R.J. Verrall. A stochastic model underlying the chain-ladder technique. ASTIN Colloquium in Cannes, pages 45–69, 1994.  |   Google Scholar
  39. P.J.R. Pinheiro, J.M.A. e Silva, and M. de Lourdes Centeno. Bootstrap methodology in claim reserving. Journal  |   Google Scholar
  40. of Risk and Insurance, (70):701–714, 2003.  |   Google Scholar
  41. G.S. Kirschner, K. Colin, and I. Belinda. Two approaches to calculating correlated reserve indications across multiple lines of business. Variance, 1:15–38, 2008.  |   Google Scholar
  42. P. England. Addendum to ’analytic and bootstrap estimates of prediction error in claims reserving’. Insurance: Mathematics and Economics, 31:461–466, 2002.  |   Google Scholar
  43. P.J.R. Pinheiro, J.M.A. e Silva, and M. de Lourdes Centeno. Bootstrap methodology in claim reserving. ASTIN  |   Google Scholar
  44. Colloquium, pages 1–13, 2001.  |   Google Scholar
  45. M.R. Shapland. Using the odp boostrap model: a practitioners guide. CAS MONOGRAPH SERIES NUMBER 4, 2016.  |   Google Scholar
  46. CAS Working Party. The analysis and estimation of loss  |   Google Scholar
  47. and alae variability: a summary report. CAS Forum, Fall: 29–146, 2005.  |   Google Scholar

Downloads

Download data is not yet available.

How to Cite

Tuysuz, S., & Pekel, P. (2019). A Comparison of Stochastic Claims Reserving Methods. European Journal of Business and Management Research, 4(4). https://doi.org/10.24018/ejbmr.2019.4.4.43

Search Panel

 Sukriye Tuysuz
 Google Scholar |   EJBMR Journal
 Pervin Pekel
 Google Scholar |   EJBMR Journal