Presentation of EAJ Issue 15/3 - January 26th

This seminar presents three distinct studies addressing key challenges in actuarial science and insurance analytics. The first study develops a framework to reconstruct true reported claim counts from observed processed claims distorted by backlogs caused by limited processing capacity. By leveraging total backlog size and stable patterns in reported claims, the approach enables accurate prediction of outstanding claims and facilitates the application of traditional reserving methods. The framework also supports cost optimization balancing processing capacity and backlog expenses, highlighting the impact of capacity constraints on claims data quality and reserving accuracy. The second study investigates mortality differences between Ireland and Northern Ireland from 2000 to 2021 using joint modeling of life tables. Employing generalized additive models (GAM) combined with Kannisto extrapolation for older ages, the analysis reveals shifting mortality patterns across age groups and regions, with Northern Ireland exhibiting higher mortality at younger and middle ages. The study underscores the need for improved national mortality tables and discusses socio-economic and healthcare system factors influencing mortality disparities. The third study surveys recent gradient boosting decision tree (GBDT) algorithms for claim frequency and severity prediction, contrasting point prediction models estimating conditional means with probabilistic models estimating full distributional parameters. The analysis demonstrates that models allowing all distributional parameters to vary with covariates yield superior adequacy compared to those assuming constant parameters except the mean. Empirical comparisons emphasize that no single algorithm universally outperforms others, reflecting the “no free lunch” theorem in machine learning. Collectively, these contributions advance methodologies for claims reserving, mortality modeling, and predictive analytics in actuarial practice. Eliciting claims development patterns and costs hidden in backlogs Random delays between the occurrence of accident events and the corresponding reporting times of insurance claims is a standard feature of insurance data. The time lag between the reporting and the processing of a claim depends on whether the claim can be processed without delay as it arrives or whether it remains unprocessed for some time because of temporarily insufficient processing capacity that is shared between all incoming claims. We aim to explain and analyze the nature of processing delays and build-up of backlogs. Development patterns for incoming reported claims that form the basis for claims reserving may be distorted by backlogs when transformed into processed (or paid) claims. In a first step, we show how to infer hidden development patterns from processed claims data. In a second step, we discuss how backlogs impact claims costs, and we show how to select processing capacity optimally in order to minimize claims costs, taking delay-adjusted costs and fixed costs for claims settlement capacity into account. Theoretical results are combined with a large-scale numerical study that demonstrates practical usefulness of our proposal. Linda Daly - Mortality in Ireland and Northern Ireland 2000–2021 and the joint modelling of Irish and Northern Irish life tables Mortality assumptions for actuarial applications in Ireland and Northern Ireland are typically set by reference to national life tables or industry specific life tables of the Continuous Mortality Investigation of the Institute Faculty of Actuaries, UK. Recent national life tables for Ireland and Northern Ireland are poor exhibiting unreasonable mortality patterns, volatile mortality rates, terminate at relatively low ages and lack coherence between the regions. This paper investigates mortality trends for Ireland and Northern Ireland for 2000–2019 and presents a method for jointly modelling the mortality of the regions over the period 2017–2019. Mortality at younger ages was modelled using Generalized Additive Models (GAMs) where mortality between the regions was implemented using difference smooths, while a Kannisto model was used to model aggregated regional mortality data at older ages. The resulting life tables provide smooth, coherent, region-specific mortality rates which extend well beyond the age range of the current life tables and provide a more appropriate basis for mortality assumptions for actuarial applications. Finally, excess mortality was used to assess the impact of the Covid-19 pandemic on the mortality of both regions for 2020–2021. Small populations experience relatively high mortality volatility which can impact estimates of excess mortality. Hence, excess mortality was calculated by reference to the jointly modelled 2017–2019 life tables and, also, by reference to projected mortality rates for 2020 and 2021 obtained by fitting a Lee-Carter model to pre-smoothed mortality rates for 2000–2019. Two dimensional GAMs were used to pre-smooth the mortality rates. From Point to Probabilistic Gradient Boosting for Claim Frequency and Severity Prediction Gradient boosting for decision tree algorithms are increasingly used in actuarial applications as they show superior predictive performance over traditional generalised linear models. Many enhancements to the first gradient boosting machine algorithm exist. We present in a unified notation, and contrast, all the existing point and probabilistic gradient boosting for decision tree algorithms: GBM, XGBoost, DART, LightGBM, CatBoost, EGBM, PGBM, XGBoostLSS, cyclic GBM, and NGBoost. In this comprehensive numerical study, we compare their performance on five publicly available datasets for claim frequency and severity, of various sizes and comprising different numbers of (high cardinality) categorical variables. We explain how varying exposure-to-risk can be handled with boosting in frequency models. We compare the algorithms on the basis of computational efficiency, predictive performance, and model adequacy. LightGBM and XGBoostLSS win in terms of computational efficiency. CatBoost sometimes improves predictive performance, especially in the presence of high cardinality categorical variables, common in actuarial science. The fully interpretable EGBM achieves competitive predictive performance compared to the black box algorithms considered. We find that there is no trade-off between model adequacy and predictive accuracy: both are achievable simultaneously.