Modelling zeros in stochastic reserving models

Kunkler, Michael

doi:10.1016/j.insmatheco.2003.09.011

Cited by 7 publications

(23 citation statements)

References 9 publications

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“…The earlier models such as de Alba (2002Alba ( , 2006 and Kunkler (2004Kunkler ( , 2006 are all aimed at solving the problem of loss reserving when either zeros or negatives appear in the loss triangle, but not both together. No model has been proposed for extending the stochastic reserving models to situations where there are both zeros and negatives existing in the loss triangle.…”

Section: A Bayesian Mixture Modelmentioning

confidence: 99%

“…Here, we will use notation consistent with that in Kunkler (2004Kunkler ( , 2006. Let y i j denote the incremental losses in the loss triangle.…”

Section: Distribution Of Mixture Datamentioning

confidence: 99%

“…So we can assume that the proportion of zeros and negatives depends only on the development year as in Kunkler (2004Kunkler ( , 2006. A Bayesian GLM for the multinomial probabilities on the development year j can be applied to model this structure.…”

Section: Generalized Linear Modelsmentioning

confidence: 99%

“…With a different factor δ ld introduced for each development year in the cumulative logistic model, the piecewise linear relationship (Kunkler, 2004(Kunkler, , 2006 gives a flexible structure. This model structure can be written as…”

Section: Generalized Linear Modelsmentioning

confidence: 99%

“…An improved Bayesian lognormal model was introduced by de Alba (2002,2006) to extend the lognormal model (Kremer, 1982) to situations where there are negative values in the loss triangle. Kunkler (2004Kunkler ( , 2006 proposed a Bayesian binomial model to handle the situation where there are either zeros or negatives in the loss triangle. None of these models, however, handle the more realistic situation when there are notable numbers of both zeros and negatives in the loss triangle.…”

Section: Introductionmentioning

confidence: 99%

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A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

Xia

Scollnik²

2015

IJSP

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In insurance loss reserving, a large portion of zeros are expected at the later development periods of an incremental loss triangle. Negative losses occur frequently in the incremental loss triangle due to actuarial practices such as subrogation and salvation. The nature of the distributions assumed by most stochastic models, such as the lognormal and over-dispersed Poisson distributions, brings restrictions on the zeros and negatives appearing in the loss triangle. In this paper, we propose a Bayesian mixture model for stochastic reserving under the situation where there are both zeros and negatives in the incremental loss triangle. A multinomial regression model will be applied to model the sign of the loss data, while the lognormal distribution is assumed for the loss magnitudes of negatives and positives. Bayesian generalized linear models will be fitted for both the mixture and magnitude models. The model will be implemented using the Markov chain Monte Carlo (MCMC) techniques in BUGS. Our model provides a realistic tool for stochastic reserving in the cases of zeros and negatives.

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Section: A Bayesian Mixture Modelmentioning

confidence: 99%

“…Here, we will use notation consistent with that in Kunkler (2004Kunkler ( , 2006. Let y i j denote the incremental losses in the loss triangle.…”

Section: Distribution Of Mixture Datamentioning

confidence: 99%

Section: Generalized Linear Modelsmentioning

confidence: 99%

Section: Generalized Linear Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

Xia

Scollnik²

2015

IJSP

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Modelling negatives in stochastic reserving models

Kunkler¹

2006

Insurance: Mathematics and Economics

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Micro-level stochastic loss reserving for general insurance

Antonio

Plat

2013

Scandinavian Actuarial Journal

116

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1 This paper demonstrates the merits of loss reserving using detailed information on the development of individual claims. Apart from few exceptions, the vast literature on stochastic loss reserving is developed for data aggregated in run-off triangles. However, a triangle is a summary of an underlying, more detailed, data set. We refer to this data set at individual claim level as 'micro-level' data. A realistic micro-level data set on liability claims from a European insurance company is analyzed. We specify a stochastic model for each event in the development of a claim: the time of occurrence of the claim, the delay between occurrence and reporting of the claim to the insurance company, the occurrence of payments and their size and the final settlement of the claim. We calibrate the resulting model to historical data and use it to project the future development of open claims.Through an out-of-sample prediction exercise we show that the micro-level approach provides the actuary with detailed and valuable reserve calculations. For the case-study developed in this paper, the micro-level model outperforms the results obtained using traditional loss reserving methods based on aggregate data.

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Modelling zeros in stochastic reserving models

Cited by 7 publications

References 9 publications

A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

Modelling negatives in stochastic reserving models

Micro-level stochastic loss reserving for general insurance

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