Prediction Error of the Chain Ladder Reserving Method applied to Correlated Run-off Triangles

In Buchwalder et al. (2006) we revisited Mack's (1993) and Murphy's (1994) estimates for the mean square error of prediction (MSEP) of the chain ladder claims reserving method. This was done using a time series model for the chain ladder method. In this paper we extend the time series model to determine an estimate for the MSEP of a portfolio of N correlated run-off triangles. This estimate differs in the special case N = 2 from the estimate given by Braun (2004). We discuss the differences between the estimate

Clustering driving styles via image processing

It has become of key interest in the insurance industry to understand and extract information from telematics car driving data. Telematics car driving data of individual car drivers can be summarized in so-called speed acceleration heatmaps. The aim of this study is to cluster such speed acceleration heatmaps to different categories by analysing similarities and differences in these heatmaps. Making use of local smoothness properties, we propose to process these heatmaps as RGB images. Clustering can then be achieved by involving supervised information via a transfer learning approach using the pre-trained AlexNet to extract discriminative features. The K-means algorithm is then applied on these extracted discriminative features for clustering. The experiment results in an improvement of heatmap clustering compared to classical approaches

Mean Square Error of Prediction in the Bornhuetter-Ferguson Claims Reserving Method

The prediction of adequate claims reserves is a major subject in actuarial practice and science. Due to their simplicity, the chain ladder (CL) and Bornhuetter-Ferguson (BF) methods are the most commonly used claims reserving methods in practice. However, in contrast to the CL method, no estimator for the conditional mean square error of prediction (MSEP) of the ultimate claim has been derived in the BF method until now, and as such, this paper aims to fill that gap. This will be done in the framework of generalized linear models (GLM) using the (overdispersed) Poisson model motivation for the use of CL factor estimates in the estimation of the claims development patter

Reversible jump Markov chain Monte Carlo method for parameter reduction in claims reserving

We present an application of the reversible jump Markov chain Monte Carlo (RJMCMC) method to the important problem of setting claims reserves in general insurance business for the outstanding loss liabilities. A measure of the uncertainty in these claims reserves estimates is also needed for solvency purposes. The RJMCMC method described in this paper represents an improvement over the manual processes often employed in practice. In particular, our RJMCMC method describes parameter reduction and tail factor estimation in the claims reserving process, and, moreover, it provides the full predictive distribution of the outstanding loss liabilities

On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins

This paper brings together analytic and simulation-based approaches to reserve risk in general (P&C) insurance, applied to the traditional actuarial view of risk over the lifetime of the liabilities and to the one-year view of Solvency II. It also connects the lifetime and one-year views of risk. The framework of the model in Mack (1993) is used throughout, although the results have wider applicability. The advantages of a simulation-based approach are highlighted, giving a full predictive distribution, which is used to estimate risk margins under Solvency II and risk adjustments under IFRS 17. We discuss methods for obtaining capital requirements in a cost-of-capital risk margin, and methods for estimating risk adjustments using risk measures applied to a simulated distribution of the outstanding liabilities over their lifetime

The impact of disease severity on the psychological well-being of youth affected by an inborn error of metabolism and their families: A one-year longitudinal study.

Inborn errors of metabolism (IEMs) refer to rare heterogeneous genetic disorders with various clinical manifestations that can cause serious physical and psychological sequelae. Results of previous studies on the impact of an IEM on health-related quality of life (HR-QoL) were incongruent and only few studies considered more broadly the psychological well-being of children with IEM and their families. Our objectives were to examine: (1) the impact of the IEM severity on the HR-QoL and psychological functioning of patients and their parents at baseline; and (2) its evolution over time; and (3) the correlation between parental and children's perspectives. Methods: The sample included 69 pediatric patients (mean age = 7.55 y, SD = 4.59) with evaluations at baseline and after one year. We collected data on HR-QoL, child mental health and emotional regulation as well as on parental mood and stress using different validated questionnaires. IEM severity was rated by a clinician through the biological subdomain of the pediatric INTERMED instrument. Results: Two groups of patients based on IEM severity scores were created (n = 31 with low and n = 38 with moderate/high IEM severity). The two groups differed with respect to age, diet and supplement intake. IEM severity had an impact on HR-QoL and behavioral symptoms in children, as well as on HR-QoL and stress in parents. For patients with moderate/high IEM severity, child and parental HR-QoL improved after 1-year of follow-up. We did not observe any significant difference between evaluations by patients versus parents. Conclusions: Our findings demonstrate that moderate/high IEM severity altered child and parental psychological well-being, but also revealed a significant improvement after one-year follow-up. This observation suggests that patients with a moderate/high IEM severity and their families benefit from the care of an interdisciplinary team including a child psychologist specialized in IEMs. Moreover, in patients with higher IEM severity there may also be more room for improvement compared to patients with low IEM severity. Future studies should focus on observations over a larger time span, particularly during adolescence, and should include objective measurements

Sensitivity-based measures of discrimination in insurance pricing

Different notions of fairness and discrimination have been extensively discussed in the machine learning and insurance pricing literatures. As not all fairness criteria can be concurrently satisfied, it is important to develop metrics that allow the assessment of materiality of discriminatory effects and the trade-offs between various criteria. Methods from sensitivity analysis have been deployed for the measurement of demographic unfairness, that is, the statistical dependence of risk predictions on protected attributes. We produce a sensitivity-based measure for the different phenomenon of proxy discrimination, referring to the implicit inference of protected attributes from other covariates. For this, we first define a set of admissible prices that avoid proxy discrimination. Then, the measure is defined as the normalised L2 -distance of a price from the closest element in that set. Furthermore, we consider the attribution of theproxy discrimination measure to individual (or subsets of) covariates and investigate how properties of the data generating process are reflected in those metrics. Finally, we build on the global (i.e., portfolio-wide) measures of demographic unfairness and proxy discrimination to propose local (i.e., policyholder-specific) measures, which allow a fine-grained understanding of discriminatory effects across a collective of policyholders