Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-29T10:58:25.694Z Has data issue: false hasContentIssue false
  • English
  • Français

A Simulation Procedure for Comparing Different Claims Reserving Methods

Published online by Cambridge University Press:  29 August 2014

Teivo Pentikäinen  and
Jukka Rantala
Teivo Pentikäinen*
Affiliation:
Finland
Jukka Rantala*
Affiliation:
Finland
*
Kasavuorentie 12 C 9, 02700 Kauniainen, Finland.
Pohjola, Ins.Co, Lapinmäentie 1, 00300 Helsinki, Finland.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The estimation of outstanding claims is one of the important aspects in the management of the insurance business. Various methods have been widely dealt with in the actuarial literature. Exploration of the inaccuracies involved is traditionally based on a post-facto comparison of the estimates against the actual outcomes of the settled claims. However, until recent years it has not been usual to consider the inaccuracies inherent in claims reserving in the context of more comprehensive (risk theoretical) models, the purpose of which is to analyse the insurer as a whole. Important parts of the technique which will be outlined in this paper can be incorporated into over-all risk theory models to introduce the uncertainty involved with technical reserves as one of the components in solvency and other analyses (Pentikäinen et al. (1989)).

The idea in this paper is to describe a procedure by which one can explore how various reserving methods react to fictitious variations, fluctuations, trends, etc. which might influence the claims process, and, what is most important, how they reflect on the variables indicating the financial position of the insurer. For this purpose, a claims process is first postulated and claims are simulated and ordered to correspond to an actual handling of the observed claims of a fictitious insurer. Next, the simulation program will ‘mime’ an actuary who is calculating the claims reserve on the basis of these ‘observed’ claims data. Finally, the simulation is further continued thus generating the settlement of the reserved claims. The difference between reserved amounts and settled amounts gives the reserving (run-off) error in this particular simulated case. By repeating the simulation numerous times (Monte Carlo method) the distribution of the error can be estimated as well as its effect on the total outcome of the insurer.

Keywords

Claims reservingrun-off errorschain laddermodel errorsparameter errorssimulation
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 22 , Issue 2 , November 1992 , pp. 191 - 216
Copyright
Copyright © International Actuarial Association 1992

References

Ashe, F. (1986) An essay at measuring the variance of estimates of outstanding claims payments. ASTIN Bulletin.Google Scholar
Beard, R. E., Pentikäinen, T. and Pesonen, E. (1984) Risk theory, (rewritten) 3. edition, Chapman and Hall, London and New York.CrossRefGoogle Scholar
Benktander, G. (1976) An approach to credibility in calculating IBNR for casualty excess Reinsurance. The Actual Review.Google Scholar
Claims Reserving Manual (1989) Institute of Actuaries. London.Google Scholar
Coutts, S., Devitt, E. R. F. and Ross, G. A. (1984) A probabilistic approach to assessing the financial strength of a general insurance company. Transactions of the International Congress of Actuaries.Google Scholar
Daykin, C., Devitt, E. R., Khan, M.R. and McCaughan, J. P. (1984) The solvency of general insurance companies. Journal of the Institute of Actuaries.CrossRefGoogle Scholar
Daykin, C., Bernstein, G.D., Coutts, S. M., Devitt, E. R., Hey, G.B., Reynolds, D.I.W. and Smith, P.D. (1987a) Assessing the solvency and financial strength of a general insurance company. Journal of the Institute of Actuaries 114: II, 1987, 227–325.CrossRefGoogle Scholar
Daykin, C., Bernstein, G.D., Coutts, S.M., Devitt, E.R., Hey, G.B., Reynolds, D.I.W. and Smith, P.D. (1987b) The solvency of general insurance company in terms of emerging costs. ASTIN Bulletin.Google Scholar
Daykin, C. D. and Hey, G. B. (1989) A practical risk theory model for the management uncertainty in an general insurance company. ASTIN Colloquium, New York.Google Scholar
Daykin, C.D. and Hey, G. B. (1990) Managing uncertainty in a general insurance company. Institute of Actuaries.Google Scholar
van Eeghen, J. (1981) Loss reserving methods. Surveys of Actuarial Studies 3, Nationale-Nederlanden N.V., Rotterdam.Google Scholar
Hewitt, C. C. (1986) Discussion contribution on claims reserves. Insurance: Mathematics and Economics.Google Scholar
Hovinen, E. (1981) Additive and Continuous IBNR. Presented in ASTIN Colloquium.Google Scholar
Norberg, R. (1986) A contribution to modelling of IBNR claims. Scandinavian Actuarial Journal.CrossRefGoogle Scholar
Pentikäinen, T. (1987) Approximative evaluation of the distribution function. ASTIN Bulletin.Google Scholar
Pentikäinen, T. and Rantala, J. (1986) Run-off risk as a part of claims fluctuation. ASTIN Bulletin.Google Scholar
Pentikäinen, T., Bonsdorff, H., Pesonen, M., Rantala, J. and Ruohonen, M. (1989) Insurance solvency and financial Strength. Finnish Training and Publishing Company Ltd, Helsinki.Google Scholar
Renshaw, A.E. (1989) Chain ladder and interactive modelling (Claims reserving and GLIM). Journal of the Institute of Actuaries Vol. 116: III, 559–587.CrossRefGoogle Scholar
Stanard, J.N. (1986) A simulation test of prediction errors of loss reserve estimation techniques. Proceedings of the Casualty Actuarial Society Vol. LXXII.Google Scholar
Sundt, B. (1990) On prediction of unsettled claims. Nordisk Försäkringstidskrift.Google Scholar
Taylor, G.C. (1986) Claims Reserving in Non-life Insurance. North Holland, Amsterdam.Google Scholar
Verrall, R.J. (1989) State space representation of the Chain Ladder linear model. Journal of the Institute of Actuaries Vol. 116: III, 589–609.CrossRefGoogle Scholar
Verrall, R.J. (1990) Bayes and empirical Bayes estimation for the Chain Ladder model. ASTIN Bulletin.Google Scholar
Wilkie, A. (1984) A stochastic investment model for actuarial use. Faculty of Actuaries.Google Scholar
Wright, (1990) A stochastic method for claims reserving in general insurance. Journal of the Institute of Actuaries Vol. 117, 677–731.CrossRefGoogle Scholar