Predicting Ibnyr Events and Delays: I. Continuous Time

Jewell, William S.

doi:10.2143/ast.19.1.2014914

Cited by 70 publications

(93 citation statements)

References 8 publications

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“…We extend the model considered in Jewell [1,2] to an inhomogeneous marked Poisson point process. We define Λ(t) ≥ 0 to be the instantaneous claims frequency and w(t) ≥ 0 to be the instantaneous exposure at time t ≥ 0.…”

Section: Individual Claims Arrival Modelingmentioning

confidence: 99%

“…We study this reporting delay function in continuous time based on real individual claims data. The data is used to calibrate a non-stationary version of the statistical model considered in Jewell [1,2]. This calibration then provides an estimation of the number of incurred but not yet reported (IBNYR) claims.…”

Section: Introductionmentioning

confidence: 99%

“…The second building block in claims reserving is the modeling of the cost process of insurance claims. 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].…”

Section: Introductionmentioning

confidence: 99%

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Understanding Reporting Delay in General Insurance

Verrall

Wüthrich

2016

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Abstract:The aim of this paper is to understand and to model claims arrival and reporting delay in general insurance. We calibrate two real individual claims data sets to the statistical model of Jewell and Norberg. One data set considers property insurance and the other one casualty insurance. For our analysis we slightly relax the model assumptions of Jewell allowing for non-stationarity so that the model is able to cope with trends and with seasonal patterns. The performance of our individual claims data prediction is compared to the prediction based on aggregate data using the Poisson chain-ladder method.

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Section: Individual Claims Arrival Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Understanding Reporting Delay in General Insurance

Verrall

Wüthrich

2016

Risks

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“…Neste trabalho trataremos como IBNR somente a quarta componente da lista acima, que tambéḿ e chamada de IBNR Pura ou verdadeira IBNR ou IBNYR(Incurred But Not Yet Reported). Os demais itens que compõem a IBNR em seu sentido abrangente, são componentes do chamado IBNER(Incurred But Not Enough Reported) ou RBNS(Reported But Not Settled) ou IBNFR(Incurred But Not Fully Reported) (4). No Brasil a IBNER foi usualmente chamada de ajuste PSL(Provisão de Sinistros a Liquidar), já que esta medidaé usada para ajustar a reserva para pagamento de sinistros já avisados porém não liquidados.…”

Section: Reserva De Sinistros Não Pagos E a Ibnrunclassified

“…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) …”

Section: Processo Poisson Marcado Com Posição Dependenteunclassified

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

SOUZA¹

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Gomes de Souza, Luciene; de Lima Veiga Filho,Álvaro(Orientador).Comparison of methods of micro-data and run-off triangle for prediction amount of IBNR. Rio de Janeiro, 2013. 83p. MSc. Dissertation -Departamento de Engenharia Elétrica, Pontifícia Universidade Católica do Rio de Janeiro.The IBNR reserve is a reserve of paramount importance for insurers. Its calculation has been accomplished by methods, mostly, deterministic, traditionally applied to claims grouped information in a particular format called run-off triangle . This method of calculation was very adequate for decades because of its simplicity and the limited computational processing capacity existing in the past. Today, with the breakthrough of this capacity, no waiver to investigating relevant information that may be lost with grouping data would be need. Many flaws of the traditional methods has been mentioned in the literature and the use of detailed information has been pointed as a form of overcoming these deficiencies. Another frequent aim in methodologies proposed for the calculation of IBNR is get a good measure of the accuracy of the estimates obtained by them and that is another expectation about the use of detailed data, since if you got more data you could get better measures.Inspired by some articles already published with proposals for modeling such not grouped data, this dissertation proposes a new model and evaluate its predictive ability and gain of knowledge about the process of occurrence and notice of the claim against that one can get from the traditional methods applied to data of amount of claims for obtain the amount of IBNR claims and their distribution. IntroduçãoA sigla IBNR (Incurred but not reported) identifica uma importante reserva que deve ser constituída pelas companhias de seguro em geral em todos os seguimentos. Esta reserva, em um determinado instante de tempo t, deve corresponder ao montante necessário para o pagamento de indenizações de todos os sinistros já ocorridos, porém ainda não informadosà seguradora.Portanto, a IBNRé definida através de uma estimativa dos sinistros ainda não observados.Rob Kaas et al.(1) afirmam que há décadas atrás, as carteiras de seguros não-vida eram financiadas através de um sistema "pay-as-you-go". Todas as reivindicações em um determinado ano eram pagas a partir da receita de prêmios do mesmo ano, independentemente do ano de origem do sinistro. Ganhos e perdas técnicas surgiram devidoà diferença entre a receita de prêmios em um ano e os sinistros pagos durante o ano. A IBNR busca antecipar o custo dos sinistros de responsabilidade da seguradora, porém ainda não conhecidos, reduzindo essas perdas e ganhos, e assim fazendo com que balanço financeiro do portfólio de cada ano seja mais próximo do real e sempre haja recursos para cobrir as indenizações a serem pagas. Diversos autores enfatizam a importância da precisão da estimativa da reserva IBNR. Segundo Friedland(2) podemos ver a importância da acurácia da estimativa de sinistros não pagos em geral por 3 pontos de vista, a ...

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B ayesian Claims Reserving

Alba

2004

Encyclopedia of Actuarial Science

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Claims reserving methods are usually classified as stochastic or nonstochastic (deterministic) depending on whether or not they allow for random variation. Bayesian methods fall within the first class. Being stochastic, they allow the actuary to carry out statistical inference of reserve estimates as opposed to deterministic models, like the traditional chain‐ladder. As an inference process, the Bayesian approach is an alternative to classical or frequentist statistical inference. From a theoretical point of view, Bayesian methods have an axiomatic foundation and are derived from first principles. From a practical perspective, Bayesian inference is the process of fitting a probability model to a set of data and summarizing the result by a probability distribution on the parameters of the model and on unobserved quantities, such as predictions for new observations.

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Predicting Ibnyr Events and Delays: I. Continuous Time

Cited by 70 publications

References 8 publications

Understanding Reporting Delay in General Insurance

Understanding Reporting Delay in General Insurance

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

B ayesian Claims Reserving

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