Claims Reserving Manual, vol.2: Section B: Description of stochastic models

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Section 2B of the Supplementary Introduction to Volume 1 gives a general description of reserving methodology. In that description, the process of arriving at an estimate of future payments is described as one of constructing a model, fitting it to some set of past observations, and using it to infer results about the future — in this case, the future events we are interested in are the payment of claims. Several distinctions are made between different types of model, including those between deterministic and stochastic models.

Deterministic reserving models are, broadly, those which only make assumptions about the expected value of future payments. Stochastic models also model the variation of those future payments. By making assumptions about the random component of a model, stochastic models allow the validity of the assumptions to be tested statistically, and produce estimates not only of the expected value of the future payments, but also of the variation about that expected value.

All the methods in Volume 2 could be described as stochastic to a greater or lesser extent. One can distinguish between them a little, since the methods described in Sections D1, D4, D5, D6 and D7 all allow the user to make estimates of the variation about the expected future payments. The methods described in sections D2 and D3, however, simply involve the fitting of curves to sets of data. The curves are then used to predict future payments, but do not allow the modeller to make estimates of the variation of these payments.

A further distinction can be made between those models based on individual claims, and those which project grouped claims data. This distinction is most commonly found amongst stochastic methods, although the only methods presently in Volume 2 which model individual claims information are those explained in Sections D4 and D7.