Strategies for Modeling Loss Development: Curve Fitting, Credibility, and Layer Adjustments

By Uri A. Korn

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Abstract

This paper discusses some strategies to better handle the model­ing of loss development patterns. Some improvements to current curve­ and distribution­fitting strategies are shown, including the use of smoothing splines to help the modeled patterns better fit the data. A strategy is shown for applying credibility to these curves that produces results that are well­behaved and that can be implemented without the use of Bayesian software. Next, it is shown how the fitted models can be leveraged to help determine the optimal look­back period to use for selecting LDFs as well as to calculate the parameter and process error distributions. Lastly, a technique is demonstrated for making adjustments to LDFs for different limits, loss caps, and attach­ment points.

Keywords: Loss development factors, credibility, generalized additive models, splines

Citation

Korn, Uri A., "Strategies for Modeling Loss Development: Curve Fitting, Credibility, and Layer Adjustments," Variance 11:1, 2018, pp. 95-117.

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Mission Statement

Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.