个人索赔准备金：一种补充方法

1February 2024 Individual claim reserving:A complementary approach to aggregated methods2February 20242.Individual models are complex compared to aggregate methods and furthermore the parametric model is sensitive to howpayments are structured or specified in the model and to the composition of the base in terms of the number of closed casesand RBNS. These models are therefore to be preferred when the chain-ladder method proves ineffective, such as in largeclaims, but also in subsegments with high-severity variance and inherent heterogeneity.An ancillary benefit of conclusion 1, above, is that the more detailed understanding enables more informed conversations withclaims.This paper aims to provide an overview of individual reserving methods, including an in-depth review of the relevant literature. Thefocus then shifts to discussing the various implemented models and how they compare to standard methods. The paper will alsoexplore the flexibility of individual claim reserving models and the potential benefits they offer in terms of accuracy and efficiency.By covering these key topics, this paper aims to provide a valuable resource for those interested in understanding the current stateof individual reserving methods and their potential applications in the insurance industry.Different types of individual claim reserving modelsOver the course of many decades, non-life insurance actuaries have used runoff triangles to estimate future payments. Over thepast few decades, the actuarial and scientific community has developed different approaches to line-by-line reserving. Theseapproaches consider each claim individually and integrate all its characteristics to predict the ultimate. Several methods have beenproposed, each specific to a given type of claim.PARAMETRIC MODELSAn appropriate probabilistic framework for individual reserving was first introduced by (E. Arjas, 1989) and (W. S. Jewell, 1989)and followed by other studies by (R. Norberg, 1993) and (O. Hesselager, 1994). To our knowledge, (R. Norberg, 1993) and (O.Hesselager, 1994) are among the earliest papers which introduced a proper probabilistic setting for individual claim reserving,recently applied by (K. Antonio and R. Plat, 2014).When we look at IBNRs, the time between the date of occurrence of the claim and the time of reporting is a crucial element in thestudy. More recently, ( A. Boumezoued and L. Devineau., 2017) revisit the original probabilistic formulations of (R. Norberg, 1993)and (O. Hesselager, 1994) and develop a framework for modelling the occurrence and timing of claims and then provide a coherentpresentation of modelling (with simulation and closed formulas) of IBNR.When the object of study is RBNS, the duration before claim closure and the ultimate are studied separately, as in (M. Ayuso et M.Santolino., 2008) or using a multistate model to model the development of the claim as in ( K. Antonio, E. Godecharle et R. V.Oirbeek, 2016) and in ( A. Boumezoued and L. Devineau., 2017). They provide a consistent presentation of the modelling (withsimulation and closed formulas) of individual claim histories as well as aggregate quantities as a global reserve for RBNS. Themodel is built on a core component that governs the payment path from reporting to closing.NONPARAMETRIC MODELSMachine learning techniques are very flexible for processing structured and unstructured data, so these techniques are increasinglyin demand in insurance.(M. V. Wüthrich, 2018) provides for the first time a contribution to illustrate how regression tree methods can be used in the contextof individual reserving. With the increase in the collection of individual claim data, and the improvement of storage methods andcomputing power, it becomes interesting to consider sophisticated forms of machine learning such as deep neural networks (NNs).These require few restrictions and assumptions on the data, incorporate complex nonlinear trends and have high predictiveperformance. NNs with various architectures have recently been applied to the reserve of individual claims as in (M. V. Wüthrich,2018) and (G. Taylor, 2019). Another way to look at past loss histories is to use recurrent neural networks (RNNs), a very popularclass of NNs introduced by (J. J. Hopfield, 1982). (S. Hochreiter et J. Schmidhuber, 1997) introduced long short-term memory(LSTM) networks, a class of RNNs, to avoid gradient explosion.PAYMENT-TO-PAYMENT MODELSIn contrast to the parametric models presented at the beginning of this section, where the approach considered is by developmentperiod, (M. Pigeon, 2014) proposes an individual claim reserving model in a parametric and discrete-time framework with apayment-to-payment approach. Individual claim reserving:A complementary approach to aggregated methods3February 2024The analysis of a line-by-line claim database provides better guidance forclaim handlersOur study is based on a database of the motor third party liability line of business provided by a major Fren