A generalized linear model with smoothing effects for claims reserving

Abstract

This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn this paper, we continue the development of the ideas introduced in England & Verrall (2001) by suggesting the use of a reparameterized version of the generalized linear model (GLM) which is frequently used in stochastic claims reserving. This model enables us to smooth the origin, development and calendar year parameters in a similar way as is often done in practice, but still keep the GLM structure. Specifically, we use this model structure in order to obtain reserve estimates and to systemize the model selection procedure that arises in the smoothing process. Moreover, we provide a bootstrap procedure to achieve a full predictive distribution.

Modeling the Oceanographic Impacts on the Spatial Distribution of Common Cephalopods During Autumn in the Yellow Sea

“…where HSI E is the estimated HSI of 2018 derived from the relationship of 2018, and HSI P is the predicted HSI of 2018 derived from the relationship of 2000-2017. The lower the value of MSEP for a model, the better is its performance (Björkwall et al, 2011). The spatial distribution of AI in October of 2018 was then overlaid on the predicted AMM-and GMM-based HSI maps of the same year to provide a visual comparison.…”

Applying State Space Models to Stochastic Claims Reserving

“…The first model is of the log-normal type applying the ANOVA principle to the logarithmic incremental data Y ij = log X ij (see Section 2). Log-normal models applied to claims reserving can be interpreted either as smoothing models or generalized linear models (GLMs), see Björkwall et al (2011). The usual assumptions are that:…”

Reversible Jump Markov Chain Monte Carlo Method for Parameter Reduction in Claims Reserving

“…In this paper we suggest a method to replace this judgmental process with a more automatic mathematical procedure that should produce results which are at least as good as those from the manual process. Björkwall et al [1] have a very similar aim, but that paper uses bootstrapping methods and we believe that the method presented in this paper has a number of advantages. Thus, the aim is to model γ 0 , .…”