Robust bootstrap procedures for the chain-ladder method

Peremans, Kris; Segaert, Pieter; Aelst, Stefan Van; Verdonck, Tim

doi:10.1080/03461238.2016.1263236

Cited by 11 publications

(8 citation statements)

References 54 publications

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“…As discussed by Mack (1993Mack ( , 1994, Renshaw and Verrall (1998), Grize (2015), and Costa et al (2016), despite its simplicity in terms of computational implementation, the chain ladder has very interesting statistical properties under some assumptions for the IBNR data at hand. Additional and important references for the chain ladder include Kremer (1982), Verrall (1994Verrall ( , 2000, Verrall (1998, 2001), Taylor (2000), Wüthrich andMerz (2008), andPeremans, Segaert, Aelst, andVerdonck (2017).…”

Section: Review Of the Literature On Ibnr Reserve Forecastingmentioning

confidence: 99%

State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects

Costa

Pizzinga

2019

Journal of Forecasting

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The issue of modeling and forecasting IBNR (incurred but not reported) actuarial reserve under Kalman filter techniques and extensions, using data arranged in a runoff triangle, is a frequent theme in the literature. One quite recent approach is to order the runoff triangle under a row-wise fashion and use linear state-space models for the resulting data set. To allow new possibilities for short-term IBNR reserves as well as to mitigate insolvency risk, in this paper we extend such a state-space method by: (i) a calendar year IBNR reserve prediction; and (ii) a tail effect for the row-wise ordered triangle. The extension is implemented with a real runoff triangle and compared with some traditional IBNR predictors. Empirical results indicate that the approach of this paper outperforms the competing methods in terms of out-of-sample comparisons and gives more conservative IBNR reserves than the original statespace method.

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Section: Review Of the Literature On Ibnr Reserve Forecastingmentioning

confidence: 99%

State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects

Costa

Pizzinga

2019

Journal of Forecasting

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“…These estimates affect the bootstrap distribution leading to unreliable inference. Therefore, we use the fast and robust bootstrap introduced by Salibian- Barrera and Zamar (2002) and generalized in e.g., and Peremans et al (2017).…”

Section: Fast and Robust Bootstrapmentioning

confidence: 99%

Robust inference for seemingly unrelated regression models

Peremans

Aelst²

2018

Journal of Multivariate Analysis

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Seemingly unrelated regression models generalize linear regression models by considering multiple regression equations that are linked by contemporaneously correlated disturbances. Robust inference for seemingly unrelated regression models is considered. MM-estimators are introduced to obtain estimators that have both a high breakdown point and a high normal efficiency. A fast and robust bootstrap procedure is developed to obtain robust inference for these estimators. Confidence intervals for the model parameters as well as hypothesis tests for linear restrictions of the regression coefficients in seemingly unrelated regression models are constructed. Moreover, in order to evaluate the need for a seemingly unrelated regression model, a robust procedure is proposed to test for the presence of correlation among the disturbances. The performance of the fast and robust bootstrap inference is evaluated empirically in simulation studies and illustrated on real data.

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“…This method has already been considered in the area of claims reserving by (England and Verrall 1999;Lowe 1994;Maciak et al 2022;Zaçaj et al 2022). Several authors ( Peremans et al 2017;Verdonck et al 2009) applied robust bootstrap procedures for the chain-ladder method.…”

Section: Introductionmentioning

confidence: 99%

Heat Equation as a Tool for Outliers Mitigation in Run-Off Triangles for Valuing the Technical Provisions in Non-Life Insurance Business

Barlak

Bakoň

Rovňák

et al. 2022

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Estimating outstanding claims reserves in the non-life insurance business is often impaired by outlier-contaminated datasets. Widely used methods to eliminate outliers in non-life development triangles are either limiting the number of outliers by robust statistical methods or by change of development factors. However, the whole estimation process is likewise adversely affected so that: (i) the total sum of all triangle payments is not correct or (ii) the difference between the original triangle and its backward estimation via the bootstrap method is ineligible. In this paper, the properties of the heat equation are examined to obtain an outlier smoothing technique for development triangles. The heat equation in two dimensions is being applied on an outlier contaminated dataset where no individual data are available. As a result, we introduce a new methodology to (i) treat outliers in non-life development triangles, (ii) keep the total sum of all triangle payments, and (iii) provide acceptable differences between the original and the backward estimated triangle. Consequently, the outlying values are eliminated and the resulting development triangle could be used as an input for any claims reserving method without a need for further robustification or change of development factors. Additionally, the research on the application of heat equation in one dimension presented in this paper enables one to employ the bootstrap method using Pearson’s residuals in cases where the method was originally inapplicable due to development factors being lower than one.

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Robust bootstrap procedures for the chain-ladder method

Cited by 11 publications

References 54 publications

State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects

State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects

Robust inference for seemingly unrelated regression models

Heat Equation as a Tool for Outliers Mitigation in Run-Off Triangles for Valuing the Technical Provisions in Non-Life Insurance Business

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