Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-12T10:36:53.967Z Has data issue: false hasContentIssue false
  • English
  • Français

Credibility Using Semiparametric Models

Published online by Cambridge University Press:  29 August 2014

Virginia R. Young
Virginia R. Young*
Affiliation:
School of Business, University of Wisconsin-Madison
*
School of Business, 975 University Avenue, University of Wisconsin-Madison, Madison, WI, USA53706
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.

To use Bayesian analysis to model insurance losses, one usually chooses a parametric conditional loss distribution for each risk and a parametric prior distribution to describe how the conditional distributions vary across the risks. A criticism of this method is that the prior distribution can be difficult to choose and the resulting model may not represent the loss data very well. In this paper, we apply techniques from nonparametric density estimation to estimate the prior. We use the estimated model to calculate the predictive mean of future claims given past claims. We illustrate our method with simulated data from a mixture of a lognormal conditional over a lognormal prior and find that the estimated predictive mean is more accurate than the linear Bühlmann credibility estimator, even when we use a conditional that is not lognormal.

Keywords

Kernel density estimationclaim estimationBayesian estimation
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 27 , Issue 2 , November 1997 , pp. 273 - 285
Copyright
Copyright © International Actuarial Association 1997

References

REFERENCES

Bühlmann, H. (1967), Experience rating and credibility, ASTIN Bulletin, 4: 199–207.CrossRefGoogle Scholar
Bühlmann, H. (1970), Mathematical Models in Risk Theory, Springer-Verlag, New York.Google Scholar
Bühlmann, H. and Straub, E. (1970), Glaubwürdigkeit für Schadensätze, Mitteilungen der Vereinigung Schweizerischer Versicherungs-Mathematiker, 70: 111–133.Google Scholar
De Groot, M. H. (1970), Optimal Statistical Decisions, McGraw-Hill, New York.Google Scholar
Hachemeister, C. A. (1975), Credibility for regression models with application to trend, 129-163, in Credibility: Theory and Applications, (ed. Kahn, P. M.), 129–163, Academic Press, New York.Google Scholar
Herzog, T. L. (1996), Introduction to Credibility Theory, second edition, ACTEX, Abington, Connecticut.Google Scholar
Jones, M. C., Marron, J. S., and Sheather, S. J. (1996), A brief survey of bandwidth selection for density estimation, Journal of the American Statistical Association, 91: 401–407.CrossRefGoogle Scholar
Klugman, S. A. (1992), Bayesian Statistics in Actuarial Science with Emphasis on Credibility, Kluwer, Boston.CrossRefGoogle Scholar
Serfling, R. J. (1980), Approximation Theorems of Mathematical Statistics, Wiley, New York.CrossRefGoogle Scholar
Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, Chapman & Hall, London.Google Scholar
Thompson, J. R. and Tapia, R. A. (1990), Nonparametric Function Estimation, Modeling, and Simulation, Society for Industrial and Applied Mathematics, Philadelphia.CrossRefGoogle Scholar
Walker, A. M. (1969), On the asymptotic behaviour of posterior distributions, Journal of the Royal Statistical Society, Series B, 31: 80–88.Google Scholar
Willmot, G. E. (1994), Introductory Credibility Theory, Institute of Insurance and Pension Research, University of Waterloo, Waterloo, Ontario.Google Scholar
Young, V. R. (1997), Credibility using a loss function from spline theory: Parametric models with a one-dimensional sufficient statistic, to appear. North American Actuarial Journal.Google Scholar