Abstract
For as long as anyone remembers non-life insurance companies have used the so called chain ladder method to reserve for outstanding liabilities. When historical payments of claims are used as observations then chain ladder can be understood as estimating a multiplicative model. In most non-life insurance companies a mixture of paid data and expert knowledge, incurred data, is used as observations instead of just payments. This paper considers recent statistical cash flow models for asset–liability hedging, capital allocation and other management decision tools, and develops two new such methods incorporating available incurred data expert knowledge into the outstanding liability cash flow model. These two new methods unbundle the incurred data to aggregates of estimates of the future cash flow. By a re-distribution to the right algorithm, the estimated future cash flow is incorporated in the overall estimation process and considered as data. A statistical validation technique is developed for these two new methods and they are compared to the other recent cash flow methods. The two methods show to have a very good performance on the real-life data set considered.
Highlights
The non-life insurance business is an important part of the economy for most developed countries with market revenues amounting to around five percent of GNP’s
This paper has developed two new methods combining classical chain ladder methodology with expert knowledge via the double chain ladder methodology
Validation is introduced for these two new methods and they are compared to the previous methods DCL, Bornhutter-Ferguson double chain ladder (BDCL), IDCL and PDCL
Summary
The non-life insurance business is an important part of the economy for most developed countries with market revenues amounting to around five percent of GNP’s. Double chain ladder, introduced in Martınez-Miranda et al (2012), builds on micro-structural assumptions but does not need granular data in the estimation procedure It is based on the methods of Verrall et al (2010) and Martınez-Miranda et al (2011) where the objective was to only rely on data that is already available in most reserving departments. Two other methods of incorporating expert knowledge of incurred data into these full cash flow models have been introduced in Martınez-Miranda et al (2013b) and Hiabu et al (2016) The first of these two methods is extracting the inflation of the cost of a single claim from the incurred data and incorporates that information in the double chain ladder model of Martınez-Miranda et al (2012).
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