On bootstrap estimators of some prediction accuracy measures of loss reserves in a non-life insurance company

Wolny-Dominiak, Alicja; Żądło, Tomasz

doi:10.1080/03610918.2020.1740263

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…Secondly, for the problem under consideration, the Quantile of Absolute Prediction Errors (QAPE), originally proposed in [27] for small area prediction problems under the LMM and then used in [28] for the problem of prediction of the total loss reserve under the Hierarchical General Linear Model (HGLM), can be modified to the following form:…”

Section: Bootstrap Estimators Of Prediction Accuracy Measures For Claim Frequencymentioning

confidence: 99%

“…, K. This means that at least p100% of realizations of absolute prediction errors for all risk factors are smaller than or equal to QMAPE p (( Ni,T+1 ) K i=1 ). Let us introduce Algorithm 1, see [28][29][30], which will be used to estimate the prediction accuracy for the considered model, where the variability of random effects will be taken into account also for the risk factors not observed in the considered dataset.…”

Section: Bootstrap Estimators Of Prediction Accuracy Measures For Claim Frequencymentioning

confidence: 99%

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The Measures of Accuracy of Claim Frequency Credibility Predictor

Wolny-Dominiak

Żądło

2021

Sustainability

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Nowadays, the sustainability risks and opportunities start to affect strongly insurance companies in regard to the resulting additional variability of future values of variables taken into account in the decision processes. This is important especially in the era of sustainable non-life insurance promoting, among others, the use of ecological car engines or ecological systems of building heating. The fundamental issue in non-life insurance is to predict future claims (e.g., the aggregate value of claims or the number of claims for a single policy) in a heterogeneous portfolio of policies taking account of claim experience. For this purpose, the so-called credibility theory is used, which was initiated by the fundamental Bühlmann model modified to the Bühlmann–Straub model. Several modifications of the model have been proposed in the literature. One of them is the development of the relationship between the credibility models and statistical mixed models (e.g., linear mixed models) for longitudinal data. The article proposes the use of the parametric bootstrap algorithm to estimate measures of accuracy of the credibility predictor of the number of claims for a single policy taking into account new risk factors resulting from the emergence of green technologies on the considered market. The predictor is obtained for the model which belongs to the class of Generalised Linear Mixed Models (GLMMs) and which is a generalization of the Bülmann–Straub model. Additionally, the possibility of predicting the number of claims and the problem of the assessment of the prediction accuracy are presented based on a policy characterized by new green risk factor (hybrid motorcycle engine) not previously present in the portfolio. The paper presents the proposed methodology in a case study using real insurance data from the Polish market.

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Section: Bootstrap Estimators Of Prediction Accuracy Measures For Claim Frequencymentioning

confidence: 99%

Section: Bootstrap Estimators Of Prediction Accuracy Measures For Claim Frequencymentioning

confidence: 99%

The Measures of Accuracy of Claim Frequency Credibility Predictor

Wolny-Dominiak

Żądło

2021

Sustainability

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Predicting Social Inequality in Poland Using Price Dispersion on the Real Estate Market

Stachurski,

Ża̧dło,

Wolny-Dominiak

2024

Soc Indic Res

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Measuring and predicting price dispersion on the real estate market is an important issue for both investors and policymakers. Price dispersion in the housing market can be seen as an additional dimension for measuring social inequality and one of the main goals of public policies that focus on life satisfaction and the accumulation of permanent wealth. The article considers the Polish real estate market and proposes the prediction methods of four measures of dispersion. They are based on quantiles and allow overall measurement of dispersion. In the prediction of dispersion measures the plug-in predictors utylizing longitudinal mixed models are proposed. Furthermore, the ex ante prediction accuracy measure called the quantile of absolute prediction errors (QAPE) is assessed using the residual bootstrap estimators. QAPE allows for a comprehensive description of the distribution of prediction errors, thus fostering discussion of possible various market scenarios.

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On Bootstrap Algorithms in Survey Sampling

Żądło

2024

KREM

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Objective: The aim of this paper is to present bootstrap algorithms for measuring the accuracy of estimation and prediction in design-based and model-based approaches in survey sampling and small area estimation. Three proposals of prediction-mean squared error estimators are also examined. Research Design & Methods: Various bootstrap procedures are shown and used to estimate the design- and prediction-mean squared errors based on real data. Computations are supported by two R packages. Findings: Three prediction-mean squared error estimators are proposed. Implications / Recommendations: The bootstrap algorithms used in the design-based approach give similar results for the considered data for the variance estimates of the considered estimator, implying that the speed of the algorithms may be important for practitioners in cases of similar properties. The proposed estimators of the prediction mean squared error produce higher estimates than other estimators in the model-based approach, indicating a positive bias that can be interpreted as a pessimistic accuracy estimate. Contribution: All the presented bootstrap algorithms are easily applicable using two R packages available at R CRAN and GitHub. Three double bootstrap prediction-MSE estimators are proposed and analysed in the real-data application.

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On bootstrap estimators of some prediction accuracy measures of loss reserves in a non-life insurance company

Cited by 3 publications

References 21 publications

The Measures of Accuracy of Claim Frequency Credibility Predictor

The Measures of Accuracy of Claim Frequency Credibility Predictor

Predicting Social Inequality in Poland Using Price Dispersion on the Real Estate Market

On Bootstrap Algorithms in Survey Sampling

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