It may sound far fetched, but it works. Dewi James describes how the nuclear decay process can be used to describe reserving methods
ONE OF THE GREATEST difficulties in setting reserves is the measurement and communication of the inherent variability of these estimates.
The most common reserving methods are chain ladder and Bornhuetter-Fergusson. These methods take ratios of claims in successive years combined with a-priori assumptions of ultimate loss ratios to produce their results – often with ad-hoc interventions by the statistician to adjust unusual past loss development. Ratio-based approaches provide relatively little information regarding reserve or cashflow variability, nor do they give meaningful insight into the physical processes driving loss development.
The nuclear approach to reserving uses ideas that have been developed by physicists in evaluating the rate of decay of radioactive isotopes. The analogy may seem remote from the insurance arena but in fact there are some striking similarities: There is an initial “discovery” period as the nuclear decay (ie claims) process commences; this is followed by a period of high-volume process-driven activity; as the remaining non-decayed material reduces there is a tail development which increasingly reflects statistical “noise” rather than a process-driven “signal”.
These stages are directly analogous to claims occurrence, notification and settlement. In the case of insurance, the value of unpaid claims at any time is equivalent to the number of non-decayed nuclei and the rate at which unpaid claims convert to paid claims is directly equivalent to the rate of decay of radio-isotopes in a single time period.
This analogy cannot be stretched too far and our research suggests that claims reserves have some additional complexities, in particular that the decay rate can vary with time. The result of this analysis is a model which conforms to the basic nuclear decay structure, whose parameters have a physical interpretation in the context of insurance claims which is then used to model reserve variability, the variability of future cash flows and ultimate claim values.