A Bifurcation Approach for Attritional and Large Losses in Chain Ladder Calculations

Abstract

We introduce a stochastic model for the development of attritional and large claims in long-tail lines of business and present a corresponding "chain ladderlike" IBNR method which allows the use of claims payment data for attritional and claims incurred data for large losses. We derive formulas for the mean squared error of prediction and apply the method to a German motor third party liability portfolio.KEYWORDS IBNR method, chain ladder, large loss, attritional loss, mean squared error of prediction, standard error.

Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2014 Update

“…More empirical works are expected to explain the obviously inconsistent evidence. Regarding reinsurance pricing, Riegel () develops a stochastic model for proportional reinsurance pricing and the associated IBNR assessment. His model is well suited to long‐tail businesses with large losses and can be applied to paid loss triangles instead of incurred loss triangles.…”

Consideration of a structural-change point in the chain-ladder method

“…The double chain-ladder method, in which both the claim count data and the loss payment data are considered together in order to obtain robust reserve estimates, was considered in Martínez Miranda et al (2015) . Riegel (2014) recently suggested a model that is applied for loss data associated with coverages that are commonly exposed to large claims. Heberle and Thomas (2014) introduced a method to estimate loss development factors in run-off data for which fuzzy numbers are used.…”

Collective loss reserving with two types of claims in motor third party liability insurance

“…Several authors proposed reserving methods which separate large and attritional losses. See Riegel (2014Riegel ( , 2016 and the references therein. In this constext, the actuary is faced with a major technical problem: for older accident years, most large losses have already been identified whereas for more recent accident years, less developments are available and a higher percentage of large losses have not yet exceeded the threshold.…”

“…In this constext, the actuary is faced with a major technical problem: for older accident years, most large losses have already been identified whereas for more recent accident years, less developments are available and a higher percentage of large losses have not yet exceeded the threshold. This is why appropriate bifurcation techniques have been proposed by Riegel (2014Riegel ( , 2016 to treat large losses on a consistent basis. To avoid these difficulties, we separate here claims with short and long developments.…”