Statistical Foundations of Actuarial Learning and its Applications

This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice. Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus

Statistical Foundations of Actuarial Learning and its Applications

This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice. Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus

Higher Moments of the Claims Development Result in General Insurance

The claims development result (CDR) is one of the major risk drivers in the profit and loss statement of a general insurance company. Therefore, the CDR has become a central object of interest under new solvency regulation. In current practice, simple methods based on the first two moments of the CDR are implemented to find a proxy for the distribution of the CDR. Such approximations based on the first two moments are rather rough and may fail to appropriately describe the shape of the distribution of the CDR. In this paper we provide an analysis of higher moments of the CDR. Within a Bayes chain ladder framework we consider two different models for which it is possible to derive analytical solutions for the higher moments of the CDR. Based on higher moments we can e.g. calculate the skewness and the excess kurtosis of the distribution of the CDR and obtain refined approximations. Moreover, a case study investigates and answers questions raised in IAS

The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)

We revisit the famous Mack formula [2], which gives an estimate for the mean square error of prediction MSEP of the chain ladder claims reserving method: We define a time series model for the chain ladder method. In this time series framework we give an approach for the estimation of the conditional MSEP. It turns out that our approach leads to results that differ from the Mack formula. But we also see that our derivation leads to the same formulas for the MSEP estimate as the ones given in Murphy [4]. We discuss the differences and similarities of these derivation

Validity and reliability of the 2-minute walk test in individuals with spinal cord injury

STUDY DESIGN Multicentre-observational study. OBJECTIVES The 6-minute walk test (6mWT) is an established assessment of walking function in individuals with spinal cord injury (SCI). However, walking 6 min can be demanding for severely impaired individuals. The 2-minute walk test (2mWT) could be an appropriate alternative that has already been validated in other neurological disorders. The aim of this study was to assess construct validity and test-rest reliability of the 2mWT in individuals with SCI. In addition, the influence of walking performance on sensitivity to change of the 2mWT was assessed. SETTING Swiss Paraplegic Center Nottwil, Switzerland; Balgrist University Hospital, Zürich, Switzerland. METHODS Fifty individuals (aged 18-79) with SCI (neurological level of injury: C1-L3, AIS: A-D) were assessed on two test days separated by 1 to 7 days. The first assessment consisted of a 2mWT familiarization, followed by a 2mWT and 10-meter walk test (10MWT) (including the Walking Index for Spinal Cord Injury (WISCI II)) in randomized order. The second assessment consisted of 2mWT and 6mWT in randomized order. Tests were separated by at least 30 min of rest. RESULTS The interclass correlation coefficient between the 2mWT assessed on the first and second test day was excellent (r = 0.980, p < 0.001). The 2mWT correlated very strongly with the 6mWT (r = 0.992, p < 0.001) and the 10MWT (r = 0.964, p < 0.001), and moderately with the WISCI II (r = 0.571, p < 0.001). Sensitivity to change was slightly affected by walking performance. CONCLUSION The 2mWT is a valid and reliable alternative to the 6mWT to measure walking function in individuals with SCI. TRIAL REGISTRATION NCT04555759

1-Bromo-2,3,5,6-tetra­fluoro-4-nitro­benzene

In the title compound, C6BrF4NO2, the nitro group is twisted by 41.7 (3)° with reference to the arene ring mean plane. The main inter­actions stabilizing the crystal structure include O⋯Br contacts [3.150 (2) and 3.201 (2) Å], while F⋯F inter­actions are minor [2.863 (3)–2.908 (3) Å]

Market value margin via mean-variance hedging

We use mean–variance hedging in discrete time in order to value an insurance liability. The prediction of the insurance liability is decomposed into claims development results, that is, yearly deteriorations in its conditional expected values until the liability is finally settled. We assume the existence of a tradeable derivative with binary pay-off written on the claims development result and available in each development period. General valuation formulas are stated and, under additional assumptions, these valuation formulas simplify to resemble familiar regulatory cost-of-capital-based formulas. However, adoption of the mean–variance framework improves upon the regulatory approach by allowing for potential calibration to observed market prices, inclusion of other tradeable assets, and consistent extension to multiple periods. Furthermore, it is shown that the hedging strategy can also lead to increased capital efficiency

Ischemia with no obstructive coronary artery disease (INOCA): A patient self-report quality of life survey from INOCA international

Background: There is limited information available regarding evidence of ischemia with no obstructive coronary arteries (INOCA) and quality of life. Purpose: To determine associations between INOCA and self-reported physical, social, and mental health. Methods: We conducted a survey of all members (n = 1579) of the INOCA International patient support group. Current self-reported diagnosis and health measures were collected. Functional capacity was retrospectively estimated using the Duke Activity Status Index (DASI), assessing levels of activities performed prior and after symptom onset. Results: A total of 297 (20.8% response rate, 91% women) reported symptoms of chest pain, pressure, or discomfort in 92.9%. Overall, 34.4% were living with symptoms for ≥3 years before an INOCA diagnosis, and 77.8% were told their symptoms were not cardiac. Estimated functional capacity was higher prior to compared to after symptom onset (8.6 ± 1.8 METs vs 5.6 ± 1.8 METs; P &lt; 0.0001). Most respondents reported an adverse impact of symptoms on their home life (80.5%), social life (80.1%), mental health (70.4%), outlook on life (69.7%), sex life (55.9%), and their partner/spouse relationship (53.9%), while approximately three-quarters reduced their work hours or stopped work completely, 47.5% retired early, and 38.4% applied for disability. Conclusions: INOCA symptoms are associated with adverse physical, mental and social health quality of life. Increased patient awareness, physician recognition and diagnosis, and clinical trials are needed to develop evidence-based guidelines for this increasingly recognized cardiovascular disorder

Enhancing precision in human neuroscience

Human neuroscience has always been pushing the boundary of what is measurable. During the last decade, concerns about statistical power and replicability - in science in general, but also specifically in human neuroscience - have fueled an extensive debate. One important insight from this discourse is the need for larger samples, which naturally increases statistical power. An alternative is to increase the precision of measurements, which is the focus of this review. This option is often overlooked, even though statistical power benefits from increasing precision as much as from increasing sample size. Nonetheless, precision has always been at the heart of good scientific practice in human neuroscience, with researchers relying on lab traditions or rules of thumb to ensure sufficient precision for their studies. In this review, we encourage a more systematic approach to precision. We start by introducing measurement precision and its importance for well-powered studies in human neuroscience. Then, determinants for precision in a range of neuroscientific methods (MRI, M/EEG, EDA, Eye-Tracking, and Endocrinology) are elaborated. We end by discussing how a more systematic evaluation of precision and the application of respective insights can lead to an increase in reproducibility in human neuroscience

Sex differences in Quality of Life in Patients with Ischemia with No Obstructive Coronary Artery Disease (INOCA): A Patient Self-Report Retrospective Survey from INOCA International

Women with obstructive coronary artery disease (CAD) have a relatively lower quality of life (QoL) compared to men, but our understanding of sex differences in QoL in ischemia with no obstructive coronary artery disease (INOCA) is limited. We conducted a survey of patient members of INOCA International with an assessment of self-reported health measures. Functional capacity was retrospectively estimated using the Duke Activity Status Index (DASI), assessing levels of activities performed before and after INOCA symptom onset. Of the 1579 patient members, the overall survey completion rate was 21%. Women represented 91% of the respondents. Estimated functional capacity, expressed as metabolic equivalents (METs), was higher before compared to after INOCA diagnosis comparably for both women and men. For every one MET decline in functional capacity, there was a significantly greater decline in QoL for men compared with women in physical health (4.0 ± 1.1 vs. 2.9 ± 0.3 days/month, p &lt; 0.001), mental health (2.4 ± 1.2 vs. 1.8 ± 0.3 days/month, p = 0.001), and social health/recreational activities (4.1 ± 1.0 vs. 2.9 ± 0.3 days/month, p = 0.0001), respectively. In an international survey of patients living with INOCA, despite similar diagnoses, clinical comorbidities, and symptoms, INOCA-related functional capacity declines are associated with a greater adverse impact on QoL in men compared to women