Comments on Taylor's see-saw approach to claims reserving
Abstract Taylor (1981) introduces the See-Saw (SS) model for claims reserving in order to make allowance for speed of finalization. The model is applied to live data given in Taylor (1981) and there is prima facie evidence to suggest that it does well, especially in the light of comparisons of actual versus expected payments for each payment year. The purpose of the present paper is to demonstrate that from the point of view of operational forecasting, which is the object of the claims reserving exercise, the fitting of the linear SS can be improved upon. Moreover, we employ the SS as a vehicle for indicating the kind of validation tests that ought to be carried out once the parameters of a proposed model have been estimated from the data. Essentially, we indicate how the properties of the residuals may be used for diagnostic checking of the model. Many researchers involved in the claims reserving area are of the view that the data are extremely noisy especially if the model put forward only explains a small proportion of the total variation. Why not test whether this is the case? It turns out that the particular linear SS used by Taylor does not explain the signal accurately so that the balance of the variation is not entirely due to noise.
An invariance principle for the analysis of non-life insurance claims
The paper is concerned initially with the admissibility of particular claim payment models. Admissibility is restricted by the requirement that, if claims escalation is excluded, the amount of outstanding claims at any epoch of development of a generation of claims should be independent of the future speed of finalization. This simple requirement represents an invariance condition. The problem of admissibility of models can therefore be approached in the manner of invariance problems in physics. Standard techniques of variational calculus are used. This analysis takes place in §§4, 5 and 6. It makes use of a major assumption roughly along the lines that changes in speed of finalization do not lead to a substantial change in the order in which the claims of a given accident year are finalized. This type of assumption is subjected to critical scrutiny in §9 (see later in this summary). Vague assumptions of this sort have been made before (Reid, 1978: Taylor, 1981c). As a preliminary to the analysis of §§4 to 6, Section 3 spells the precise assumption being made here. Section 7 provides a brief interpretation of the admissible set of claim payment models. Each admissible model is the sum of two recognizable submodels:
General expression for the density effect for the ionization loss of charged particles
The equations for the density-effect correction $\ensuremath{\delta}(X)$ for the ionization loss as given in a previous paper have been extended to the case where $\ensuremath{\delta}({X}_{0})\ensuremath{\equiv}{\ensuremath{\delta}}_{0}g0$. Here ${X}_{0}$ is the lower limit of the range ${X}_{0}lXl{X}_{1}$, where a particularly simple expression for $\ensuremath{\delta}(X)$ applies; $X={log}_{10}(\frac{p}{{m}_{0}c})$, where $p$ is the momentum and ${m}_{0}$ is the mass of the incident particle. The case ${\ensuremath{\delta}}_{0}g0$ applies directly to the calculation of $\ensuremath{\delta}(X)$ for conductors (metals).