On unbalanced data and common shock models in stochastic loss reserving

Avanzi, Benjamin; Taylor, Greg; Vu, Phuong Anh; Wong, Bernard

doi:10.1017/s1748499520000196

Cited by 3 publications

(4 citation statements)

References 31 publications

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“…Although the papers of Avanzi et al (2016Avanzi et al ( , 2021 on balance worked in the context of claim triangles, the present paper will adopt the more general framework of Avanzi et al (2018).…”

Section: Notationmentioning

confidence: 99%

Auto-balanced common shock claim models

Taylor

Vu²

2023

Ann. actuar. sci.

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The paper is concerned with common shock models of claim triangles. These are usually constructed as linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced corrections for this. The present paper discusses “auto-balanced” models, in which all shock and idiosyncratic components contribute to observations such that their proportionate contributions are constant from one observation to another. The conditions for auto-balance are found to be simple and applicable to a wide range of model structures. Numerical illustrations are given.

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Section: Notationmentioning

confidence: 99%

Auto-balanced common shock claim models

Taylor

Vu²

2023

Ann. actuar. sci.

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“…This provides a formal basis for the non-robustness of the chain-ladder technique and related techniques. A comprehensive study of impact functions of central estimates, mean squared errors, and quantiles of reserves can be found in Avanzi et al (2023).…”

Section: Motivationmentioning

confidence: 99%

“…A comprehensive study of impact functions of central estimates, mean squared errors, and quantiles of reserves can be found in Avanzi et al . (2023).…”

Section: Introductionmentioning

confidence: 99%

Detection and treatment of outliers for multivariate robust loss reserving

Avanzi,

Lavender,

Taylor

et al. 2023

Ann. actuar. sci.

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Traditional techniques for calculating outstanding claim liabilities such as the chain-ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck & Debruyne (2011, Insurance: Mathematics and Economics, 48, 85–98) and Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188–193). In this paper, we put forward two alternative robust bivariate chain-ladder techniques to extend the approach of Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188–193). The first technique is based on Adjusted Outlyingness (Hubert & Van der Veeken, 2008. Journal of Chemometrics,22, 235–246) and explicitly incorporates skewness into the analysis while providing a unique measure of outlyingness for each observation. The second technique is based on bagdistance (Hubert et al., 2016. Statistics: Methodology, 1–23) which is derived from the bagplot; however; it is able to provide a unique measure of outlyingness and a means to adjust outlying observations based on this measure. Furthermore, we extend our robust bivariate chain-ladder approach to an N-dimensional framework. The implementation of the methods, especially beyond bivariate, is not trivial. This is illustrated on a trivariate data set from Australian general insurers and results under the different outlier detection and treatment mechanisms are compared.

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“…Datasets in non-life insurance industry are often contaminated by outliers [3]. The standard chain ladder reserving method is sensitive towards outlier data, making the estimate of the future claim inaccurate, thus posing an additional risk on the solvency of the insurance company [4]. Another method discussed by Hubert et al [5] uses the generalization of linear regression model with which the error terms are correlated.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Robust Chain Ladder Method in Estimating Australian Motor Insurance Reserves With Outlying Dataset

Johan¹,

Kusnadi²,

Yong³

2023

BAREKENG: J. Math. & App.

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Reserves are one of the most crucial components for an insurance company to make sure it has enough money to pay off all the incurred claims. The presence of outliers in the incurred claims data harbors risk on inaccurately predicting reserves to cover claim amounts, usually achieved by the standard chain ladder reserving method. To remedy the effect of the outliers, the robust chain ladder reserving method is used by setting the median value to predict estimated reserve. On this research, we utilized both methods on various datasets. The purpose of this paper is to determine the best method that can be utilized by insurance company in various scenario to obtain the most optimized reserved estimate that can minimize the risk of being unable to pay the insurance claim or even the risk of over allocating reserves that could pose profitability issue. The primary data used are the Australian domestic motor insurance claims from 2012 to 2017, obtained from Australian Prudential Regulation Authority (APRA). The dataset is then manipulated to have outliers. After calculating the estimation, the result is compared to assess the strength of the methods using Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) calculation. In conclusion, we found that the robust chain ladder reserving method works better in an outlying dataset. We also identify cases in which robust chain ladder are not appropriately used.

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On unbalanced data and common shock models in stochastic loss reserving

Cited by 3 publications

References 31 publications

Auto-balanced common shock claim models

Auto-balanced common shock claim models

Detection and treatment of outliers for multivariate robust loss reserving

Analysis of Robust Chain Ladder Method in Estimating Australian Motor Insurance Reserves With Outlying Dataset

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