Presentation of EAJ Issue 15/1 - 19 May 2025

Authors featured in the upcoming issue of the European Actuarial Journal present their paper's findings in a series of concise talks. The seminar will be chaired by Stephane Loisel, co-editor of the EAJ. A framework for optimal portfolios with sustainable assets and climate scenarios With the increasing impact of global warming and climate change, governments must take actions to reduce CO_2 output and to encourage more environmentally friendly industrial processes. As the use of climate scenarios is the common method in illustrating possible consequences of the climate changes, we assume that it will also be the basis for political decisions with respect to future sustainability requirements on companies and thus (directly or indirectly) for sustainability constraints for life insurance companies and pension funds. Hence, we assume that bonus/malus measures by the government will already be laid out conditioned on the finally realized climate scenario. We will therefore present a corresponding framework for optimal investment under agreed government measures for the realization of future climate scenarios. This framework is particularly suited for strategies of large institutional investors such as life insurances. It will also be illustrated by explicit examples. Modeling lower-truncated and right-censored insurance claims with an extension of the MBBEFD class In general insurance, claims are often lower-truncated and right-censored because insurance contracts may involve deductibles and maximal covers. Most classical statistical models are not (directly) suited to model lower-truncated and right-censored claims. A surprisingly flexible family of distributions that can cope with lower-truncated and right-censored claims is the class of MBBEFD distributions that originally has been introduced by Bernegger (1997) for reinsurance pricing, but which has not gained much attention outside the reinsurance literature. Interestingly, in general insurance, we mainly rely on unimodal skewed densities, whereas the reinsurance literature typically proposes monotonically decreasing densities within the MBBEFD class. We show that this class contains both types of densities, and we extend it to a bigger family of distribution functions suitable for modeling lower-truncated and right-censored claims. In addition, we discuss how changes in the deductible or the maximal cover affect the chosen distributions. A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules Risk-sharing is one way to pool risks without the need for a third party. To ensure the attractiveness of such a system, the rule should be accepted and understood by all participants. A desirable risk-sharing rule should fulfill actuarial fairness and Pareto optimality while being easy to compute. This paper establishes a one-to-one correspondence between an actuarially fair Pareto optimal (AFPO) risk-sharing rule and a fixed point of a specific function. A fast numerical method for computing these risk-sharing rules is also derived. As a result, we can compute AFPO risk-sharing rules for a large number of heterogeneous participants in this framework. An engine to simulate insurance fraud network data Traditionally, the detection of fraudulent insurance claims relies on business rules and expert judgement which makes it a time-consuming and expensive process (Óskarsdóttir et al. in Risk Anal 42(8):1872–1890, 2022). Consequently, researchers have been examining ways to develop efficient and accurate analytic strategies to flag suspicious claims. Feeding learning methods with features engineered from the social network of parties involved in a claim is a particularly promising strategy (see for example Óskarsdóttir et al. in Risk Anal 42(8):1872–1890, 2022; Van Vlasselaer et al. in Manag Sci 63(9):3090–3110, 2016; Tumminello et al. in J Risk Insur 90(2), 381–419, 2023). When developing a fraud detection model, however, we are confronted with several challenges. The uncommon nature of fraud, for example, creates a high class imbalance which complicates the development of well performing analytic classification models. In addition, only a small number of claims are investigated and get a label, which results in a large corpus of unlabeled data. Yet another challenge is the lack of publicly available data. This hinders not only the development of new methods, but also the validation of existing techniques. We therefore design a simulation machine that is engineered to create synthetic data with a network structure and available covariates similar to the real life insurance fraud data set analyzed in Óskarsdóttir et al. (Risk Anal 42(8):1872–1890, 2022). Further, the user has control over several data-generating mechanisms. We can specify the total number of policyholders and parties, the desired level of imbalance and the (effect size of the) features in the fraud generating model. As such, the simulation engine enables researchers and practitioners to examine several methodological challenges as well as to test their (development strategy of) insurance fraud detection models in a range of different settings. Moreover, large synthetic data sets can be generated to evaluate the predictive performance of (advanced) machine learning techniques. Hybrid life insurance valuation based on a new standard deviation premium principle in a stochastic interest rate framew In a complete arbitrage-free financial market, financial products are valued with the risk-neutral measure and these products are completely hedgeable. In life insurance, the approach is different as the valuation is based on an insurance premium principle which includes a safety loading. The insurer reduces the risk by pooling a vast number of independent risks. In our framework, we suggest valuations of a class of products that are dependent on both mortality and financial risk, namely hybrid life products. The main contribution of this paper is to present a generalized standard deviation premium principle in a stochastic interest rate framework, and to integrate it in different valuation operators suggested in the literature. We illustrate our methods with a classical application, namely a Pure Endowment with profit. Several numerical results are presented, and an extensive sensitivity analysis is included. Claim reserving via inverse probability weighting: a micro-level Chain-Ladder method Claim reserving primarily relies on macro-level models, with the Chain-Ladder method being the most widely adopted. These methods were heuristically developed without minimal statistical foundations, relying on oversimplified data assumptions and neglecting policyholder heterogeneity, often resulting in conservative reserve predictions. Micro-level reserving, utilizing stochastic modeling with granular information, can improve predictions, but tends to involve less attractive and complex models for practitioners. This paper aims to strike a practical balance between aggregate and individual models by introducing a methodology that enables the Chain-Ladder method to incorporate individual information. We achieve this by proposing a novel framework and formulating the claim reserving problem within a population sampling context. We introduce a reserve estimator in a frequency- and severity-distribution-free manner that utilizes inverse probability weights (IPW) driven by individual information, akin to propensity scores. We demonstrate that the Chain-Ladder method emerges as a particular case of such an IPW estimator, thereby inheriting a statistically sound foundation based on population sampling theory that enables the use of granular information and other extensions. Prediction intervals for future Pareto record claims Stochastic models and methods for quantifying extreme events are of interest in numerous disciplines. Within this paper, statistical prediction of extreme claims or losses in insurance industry is considered based on upper record values, which describe successively largest observations in a sequence of data over time. The problem of predicting a future record value (here in particular, a future record claim) based on a sequence of previously observed record values (here, past record claims) is addressed by means of prediction intervals. For an underlying Pareto distribution, respective exact and approximate intervals from the literature are summarized and modified and new ones are developed. In a simulation study, these prediction intervals are evaluated and compared regarding coverage frequency and length. The impact of the number of observed record values as well as the choice of the Pareto distribution is discussed. In the case of a small number of record values, the use of k-th record values is considered as an option for statistical analyses to predict, e.g., second largest record claims. Selected prediction methods are applied to several real data sets, which turn out to perform well and to be able to capture the magnitude of future record claims, even for fairly small numbers of record observations. For comparison, generalized Pareto distributions are fitted to real data sets and a corresponding point predictor as well as a respective upper prediction interval for the next record to appear are derived and evaluated.