Cash flow generalisations of non-life insurance expert systems estimating outstanding liabilities

• Two new reserving methods using expert opinion incurred data are presented.
• New methodology allows reserving methods to be compared via validation.
• The two most popular actuarial reserving methods can also be compared via this new method.
• Our new expert system approach to reserving is shown to be superior for our real life example.

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.