Introduction

This chapter describes several of the reserving methods that can be used to derive reserve estimates. The methods are labelled as “deterministic”, to distinguish them from stochastic methods, which are described in Chapter 4. The termdeterministic in this context is intended to mean that the method will typically produce a single or “point” estimate of the reserves, without an assessment of the statistical variability around that estimate. Such methods can, however, be used to provide a range of results by varying the assumptions used within the method.

Although deterministic methods are different in nature to stochastic methods, they are still sometimes referred to as “statistical” methods, to distinguish them from case by case type approaches, in which the reserves are determined by merely adding up all the individual case reserves for each reported claim. The use of the term statistical in this way is not intended to mean that the methods are based on a formal statistical model.

In practice, deterministic methods are used in most cases where a single point estimate of reserves is required, notwithstanding the fact that stochastic methods can also be used to produce a point estimate. For both types of method, they will usually be applied within the context of an overall reserving process, as opposed to a confined theoretical context. This process is outlined in Chapter 1. Although this chapter focuses on explaining the methods themselves, it does also include some high-level comments relating to their practical application, with additional details being given in Chapters 5, 6 and 7.

The goal of applying the reserving methods described in this chapter is assumed to be to estimate the ultimate claims and hence the corresponding Claims Reserve (as defined in Chapter 1) – that is the total amount relating to Case Reserves, IBNR and IBNER. Different methods are usually needed to derive the other types of reserve described in that chapter, such as ULAE and UPR. Where relevant, reference is made to the methods that can be used for these other reserve types in Chapter 6.

These methods are assumed to be applied to data organised in a triangle format (which was introduced in Chapter 2), and to one triangle at a time, unless stated otherwise.