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A generalized linear model with smoothing effects for claims reserving
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
2011 (Engelska)Ingår i: Insurance, Mathematics & Economics, ISSN 0167-6687, E-ISSN 1873-5959, Vol. 49, nr 1, s. 27-37Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

In this paper, we continue the development of the ideas introduced in England and 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.

Ort, förlag, år, upplaga, sidor
2011. Vol. 49, nr 1, s. 27-37
Nyckelord [en]
Bootstrap; Generalized linear model, Model selection, Smoothing, Stochastic claims reserving
Nationell ämneskategori
Matematik
Forskningsämne
matematisk statistik
Identifikatorer
URN: urn:nbn:se:su:diva-52363DOI: 10.1016/j.insmatheco.2011.01.012ISI: 000291838200004OAI: oai:DiVA.org:su-52363DiVA, id: diva2:387207
Tillgänglig från: 2011-01-13 Skapad: 2011-01-13 Senast uppdaterad: 2022-02-24Bibliografiskt granskad
Ingår i avhandling
1. Stochastic claims reserving in non-life insurance: Bootstrap and smoothing models
Öppna denna publikation i ny flik eller fönster >>Stochastic claims reserving in non-life insurance: Bootstrap and smoothing models
2011 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

In practice there is a long tradition of actuaries calculating reserve estimates according to deterministic methods without explicit reference to a stochastic model. For instance, the chain-ladder was originally a deterministic reserving method. Moreover, the actuaries often make ad hoc adjustments of the methods, for example, smoothing of the chain-ladder development factors, in order to fit the data set under analysis.

However, stochastic models are needed in order to assess the variability of the claims reserve. The standard statistical approach would be to first specify a model, then find an estimate of the outstanding claims under that model, typically by maximum likelihood, and finally the model could be used to find the precision of the estimate. As a compromise between this approach and the actuary's way of working without reference to a model the object of the research area has often been to first construct a model and a method that produces the actuary's estimate and then use this model in order to assess the uncertainty of the estimate. A drawback of this approach is that the suggested models have been constructed to give a measure of the precision of the reserve estimate without the possibility of changing the estimate itself.

The starting point of this thesis is the inconsistency between the deterministic approaches used in practice and the stochastic ones suggested in the literature. On one hand, the purpose of Paper I is to develop a bootstrap technique which easily enables the actuary to use other development factor methods than the pure chain-ladder relying on as few model assumptions as possible. This bootstrap technique is then extended and applied to the separation method in Paper II. On the other hand, the purpose of Paper III is to create a stochastic framework which imitates the ad hoc deterministic smoothing of chain-ladder development factors which is frequently used in practice.

Ort, förlag, år, upplaga, sidor
Stockholm: Department of Mathematics, Stockholm University, 2011. s. 48
Nyckelord
Bootstrap, Chain-ladder, Generalized linear model, Separation method, Smoothing, Stochastic claims reserving
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematisk statistik
Identifikatorer
urn:nbn:se:su:diva-55347 (URN)978-91-7447-255-4 (ISBN)
Disputation
2011-06-10, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (Engelska)
Opponent
Handledare
Tillgänglig från: 2011-05-12 Skapad: 2011-03-10 Senast uppdaterad: 2022-02-24Bibliografiskt granskad

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Björkwall, SusannaHössjer, Ola

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