Claims reserves are held by insurance companies so that they have sufficient funds to pay claims when they are submitted by policyholders. In general insurance, insurance policies usually last for a year; the policyholder pays an upfront premium and then expects any claims to be met - no matter when they are made. The problem for insurers is that there is often a delay before the claims are arrive, and then a further delay before they are paid. This delay can be fairly short, because it simply takes time for a claim to be made and processed. However, it can also be extremely long, with the extreme cases (such as asbestosis claims) being made many years after the policy was written. It is therefore essential for the company to hold adequate reserves to be able to meet its liabilities - this is the reason that claims reserves exist.

In recent years, a lot more attention has been given to the possible differences between the reserves and the actual outcome in terms of the claims paid. And also, there is considerable interest in the variability of the reserves from year to year: as more information becomes available, the estimates of what will have to be paid in claims may change. This is very important because it influences the amount of capital that companies are required to hold to ensure their continuing solvency. The capital that is required also shows to investors and management how profitable the business is (or different parts of the business are). For all these reasons, a lot more attention has been given to the likely variability of the claims reserves, as well as the actual amount held in these reserves. There have been many papers written on this subject, and one of the most well-known is "Stochastic Claims Reserving in General Insurance", which is attached as a pdf. This paper sets out the overall framework for stochastic reserving, and considers some of the most frequently used modelling approaches. There is also an on-line lecture (see below) which covers the material in this paper - and some other issues as well.

One of the most popular methods is bootstrapping, and this is often applied to the over-dispersed Poisson model. However, it can also be applied with any other model including the Mack model. The paper "Predictive Distributions of Outstanding Liabilities in General Insurance" describes how to apply bootstrapping to recursive models (such as the Mack model), and also covers Bayesian modelling (see also this paper ) .

Attached are a number of spreadsheets, showing how to apply the models analytically and using bootstrapping.