Single loss development models for the projection of individual Large Claims for Long Tail Non-Propo

Single loss development models for the projection of individual Large Claims for Long Tail Non-Propo

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Speaker: Steffen Schumann

Commonly used aggregate loss reserving methods, such as Chain Ladder or Cape-Cod, have the disadvantage that they do not include all the information each single loss contains. A possible solution for this are Single Loss Development (SLD) models (see Drieskens et al. (2012), Murphy, McLennan (2006), Mack (2002), Höhn, Bollmann (2006), Larsen (2007), or Norberg (1993)). Even though several SLD models exist, they are currently not widely used in practice (2016). Nevertheless, SLD models have many advantages and a big potential, e.g. they allow to estimate the severity curve based on curve fitting to ultimate single losses which is not feasible with an aggregate model.

Thus, the research focus is set on the development of a new SLD model leading to a more realistic approximation of the ultimate claims for large losses. In order to do so, the process is divided into several steps. At first, the structure of the data is analysed using methods of cluster analysis (see Kaufman, Rousseeuw (2009), Jain (2010), and Jain, Dubes (1988)). Afterwards, this information is used to build a new SLD model framework in which claims are developed according to their incurred and payment ratio value. For the projection towards the ultimate, the claims’ development range of the payment ratios and incurred values is simulated using a non-parametric Copula. Furthermore, the claims’ history and a maximal possible development range are considered. In the end, the ultimate losses and their related distribution function, as well as several key figures can be determined. Thus far, a first application on claim data has been carried out.

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