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On the relationship between classical chain ladder and granular reserving

Hiabu, M. (2016). On the relationship between classical chain ladder and granular reserving. Scandinavian Actuarial Journal, 2017(8), pp. 708-729. doi: 10.1080/03461238.2016.1240709

Abstract

We connect classical chain ladder to granular reserving. This is done by defining explicitly how the classical run-off triangles are generated from individual iid observations in continuous time. One important result is that the development factors have a one to one correspondence to a histogram estimator of a hazard running in reversed development time. A second result is that chain ladder has a systematic bias if the row effect has not the same distribution when conditioned on any of the aggregated periods. This means that the chain ladder assumptions on one level of aggregation, say yearly, are different from the chain ladder assumptions when aggregated in quarters and the optimal level of aggregation is a classical bias variance trade-off depending on the data-set. We introduce smooth development factors arising from non-parametric hazard kernel smoother improving the estimation significantly.

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article published online by Taylor & Francis in Scandinavian Actuarial Journal on 13/10/2016, available online: http://www.tandfonline.com/10.1080/03461238.2016.1240709.
Publisher Keywords: Chain ladder, granular reserving, development factors, Solvency II, non-life insurance
Subjects: H Social Sciences > HA Statistics
Departments: Cass Business School > Actuarial Science & Insurance
URI: http://openaccess.city.ac.uk/id/eprint/16953
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