AbstractsMathematics

External loss data are typically left truncated at a reporting threshold. Ignoring this truncation level leads to biased capital charge estimations. This thesis addresses the challenges of recreating the truncated part of the distribution. By predicting the continuation of a probability density function, the unobserved body of an external operational risk loss distribution is estimated. The prediction is based on internally collected losses and the tail of the external loss distribution. Using a semiparametric approach to generate sets of internal losses and applying the Best Linear Unbiased Predictor, results in an enriched external dataset that shares resemblance with the internal dataset. By avoiding any parametrical assumptions, this study proposes a new and unique way to address the reporting threshold problem. Financial institutions will benefit from these findings as it permits the use of the semiparametric approach developed by Bolancé et al. (2012) and thereby eliminates the well known difficulty with determining the breaking point beyond which the tail domain is defined when using the Loss Distribution Approach. The main conclusion from this thesis is that predicting the continuation of a function using the Best Linear Unbiased Predictor can be successfully applied in an operational risk setting. This thesis has predicted the continuation of a probability density function, resulting in a full external loss distribution.