Individual Claim Loss Reserving Conditioned by Case Estimates

Abstract

This paper examines various forms of individual claim model for the purpose of loss reserving, with emphasis on the prediction error associated with the reserve. Each form of model is calibrated against a single extensive data set, and then used to generate a forecast of loss reserve and an estimate of its prediction error.The basis of this is a model of the “paids” type, in which the sizes of strictly positive individual finalised claims are expressed in terms of a small number of covariates, most of which are in some way functions of time. Such models can be found in the literature.The purpose of the current paper is to extend these to individual claim “incurreds” models. These are constructed by the inclusion of case estimates in the model's conditioning information. This form of model is found to involve rather more complexity in its structure.For the particular data set considered here, this did not yield any direct improvement in prediction error. However, a blending of the paids and incurreds models did so.

Understanding Reporting Delay in General Insurance

“…Replacing all parameters by their MLEs given by Lemma 4 and w i Λ i = M i (which is the MLE for i ≤ m * under assumption (11)) we get an estimate for the confidence bounds (12). These are plotted in Figure 5.…”

“…Jewell [1] stated in 1989: "Currently, the development of a good model for cost evolution over continuous time appears to require a long-term research effort, one that we believe will use the basic understanding of the event generation and reporting processes developed here, but will require much additional empirical effort to develop an understanding of cost-generating mechanisms and their evolution over time." Meanwhile, there have been some improvements into this direction, see Bühlmann et al [3], Arjas [4], Norberg [5,6], Haastrup-Arjas [7], Taylor [8,9], Herbst [10], Larsen [11], Taylor et al [12], Jessen et al [13], Rosenlund [14], Pigeon et al [15], Agbeko et al [16], Antonio-Plat [17] and Badescu et al [18,19]. But we believe that state-of-the-art modeling is still far from having a good statistical model that can be used in daily industry practice.…”

An Individual Claims History Simulation Machine

“…These simulated claims then allow us to back-test classical aggregate claims reserving methods-such as the chain-ladder method-as well as to develop new claims reserving methods which are based on individual claims histories. The latter has become increasingly popular in actuarial science, see Antonio and Plat (2014), Hiabu et al (2016), Jessen et al (2011), Martínez-Miranda et al (2015), Pigeon et al (2013), Taylor et al (2008), Verrall and Wüthrich (2016) and Wüthrich (2018a) for recent developments. A main shortcoming in this field of research is that there is no publicly available individual claims history data.…”

Comparação De Métodos De Micro-Dados E De Triângulo Run-Off Para Previsão Da Quantidade Ibnr

“…England e Verrall(11) também afirmam que, dado o contínuo crescimento do poder computacional, deve-se o questionar quando não seria melhor examinar dados de sinistros individuais ao invés de agregados. Acima de tudo a principal motivação para utilização de dados não agregadosé o não desperdício de informações que podem ser preciosas para adequada estimação das reservas e possivelmente uma distribuição associada a elas (21,22,5 (38). Os métodos para obtenção da distribuição de atrasos e quantidade total de sinistros por período de ocorrência dos artigos citados neste parágrafo e da abordagem proposta serão detalhados no capítulo 3.…”

“…Nesta dissertação o interesse está nas componentes a e b das equações (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) …”