Stochastic reserving methods provide both a point estimate (e.g. a best estimate) of the future claims and an estimate of the variability surrounding that point estimate. Some of these methods also provide an estimate of the full distribution of future claims and their associated cash flows. In most practical reserving situations, if a point estimate for the reserves is required (e.g. as part of a regular reserving exercise for financial reporting purposes) this will often be determined using a combination of deterministic, as opposed to stochastic, reserving methods. Although there is no reason why stochastic methods cannot be used to derive the point estimate, in practice this is not usually the case, at least at present. Despite this, the majority of insurers will be making some use of stochastic reserving methods, in one form or another, and hence an understanding of the different methods available and their limitations is vital for most insurers.
This chapter provides a description of several stochastic reserving methods, including those that are commonly used in practice (at least in the UK in 2017), along with worked examples of these methods. There is also a brief description of other less commonly used methods and to some more recently developed approaches. Although some details of the mathematical formulation of a number of methods is included, this chapter is not intended to represent a thorough analysis of the underlying theoretical basis for the methods that are described here, but rather an overview of some of the commonly used methods. Readers who require more details of the underlying theory will find many sources in the extensive body of material that is available on stochastic reserving. Several of these sources are referred to in this chapter.
Most of the stochastic claims reserving techniques that have been developed are designed to be used where the data triangle structure is an appropriate one to use in order to estimate reserves. As discussed in Section 2.5, there are some instances where the triangle format is not the most appropriate format to use.