Portfolio Decomposition: A Building Block Approach to Loss Development

Loss development triangles are a fundamental component of the loss reserve adequacy testing process. These triangles may not be ideal for the immediate application and, almost certainly, will be less efficacious when. used for other applications. Whenever possible, the patterns and associated age-to-ultimate loss development factors disclosed by the triangles are adjusted to correct for the less than ideal correspondence between the intended application and the historical data. These adjustments are typically performed at a macroscopic level. The methods frequently begin by determining the average maturity of the data that is to be developed. This average maturity is then compared with the average maturity of the historical data as of each valuation date. If a match can be found (i.e., if the data that is to be developed has the same average maturity as the historical data at one of its valuations), then it is assumed that the corresponding age-to-ultimate loss development factor can be applied to the losses under investigation. If no match is found, the required development factor is determined by interpolating between historical valuations whose average maturities lie on either side of the required maturity. This paper presents an alternative adjustment method that is based upon a microscopic model of loss development. More specifically, losses making up the actual triangle are expressed in terms of an aggregation of the losses arising from single, infinitesimal, units of exposure. The development pattern for losses arising from these infinitesimal exposure units is modeled in such a way that it reproduces the observed macroscopic patterns. Once the model is established, the infinitesimal building blocks can be separated and recombined to reflect the aggregate losses corresponding to other groupings, at any desired valuation date.