The emergence of COVID-19 has resulted in a notable rise in mortality rates, consequently affecting various sectors, including the insurance industry. This paper analyzes the reflections of a sudden increase in mortality rates on the financial performance of a survival benefit scenario under the International Financial Reporting Standard 17. For this purpose, we thoroughly examined a single insurance scenario under four different states by modifying the interest and jump elements. We use Poisson-log bilinear Lee–Carter and Vasicek models for mortality and stochastic interest rate, respectively. Integrating the mortality model with a jump model that incorporates COVID-19 deaths we constructed a temporary mortality jump model. As a result, the temporary mortality jump model reflects the effects of the pandemic more realistically. We observe that even in this case mortality has a minor impact, whereas interest rates significantly still affect the financial position and performance of insurance companies.

We extend the growth-at-risk (GaR) literature by examining US growth risks over 130 years using a time-varying parameter stochastic volatility regression model. This model effectively captures the distribution of GDP growth over long samples, accommodating changing relationships across variables and structural breaks. Our analysis offers several key insights for policymakers. We identify significant temporal variation in both the level and determinants of GaR. The stability of upside risks to GDP growth, as seen in previous research, is largely confined to the Great Moderation period, with a more balanced risk distribution prior to the 1970s. Additionally, the distribution of GDP growth has narrowed significantly since the end of the Bretton Woods system. Financial stress is consistently associated with higher downside risks, without affecting upside risks. Moreover, indicators such as credit growth and house prices influence both downside and upside risks during economic booms. Our findings also contribute to the financial cycle literature by providing a comprehensive view of the drivers and risks associated with economic booms and recessions over time.

Forecasts play a central role in decision-making under uncertainty. After a brief review of the general issues, this article considers ways of using high-dimensional data in forecasting. We consider selecting variables from a known active set, known knowns, using Lasso and One Covariate at a time Multiple Testing, and approximating unobserved latent factors, known unknowns, by various means. This combines both sparse and dense approaches to forecasting. We demonstrate the various issues involved in variable selection in a high-dimensional setting with an application to forecasting UK inflation at different horizons over the period 2020q1–2023q1. This application shows both the power of parsimonious models and the importance of allowing for global variables.

High-cardinality categorical features are pervasive in actuarial data (e.g., occupation in commercial property insurance). Standard categorical encoding methods like one-hot encoding are inadequate in these settings.

In this work, we present a novel Generalised Linear Mixed Model Neural Network (“GLMMNet”) approach to the modelling of high-cardinality categorical features. The GLMMNet integrates a generalised linear mixed model in a deep learning framework, offering the predictive power of neural networks and the transparency of random effects estimates, the latter of which cannot be obtained from the entity embedding models. Further, its flexibility to deal with any distribution in the exponential dispersion (ED) family makes it widely applicable to many actuarial contexts and beyond. In order to facilitate the application of GLMMNet to large datasets, we use variational inference to estimate its parameters—both traditional mean field and versions utilising textual information underlying the high-cardinality categorical features.

We illustrate and compare the GLMMNet against existing approaches in a range of simulation experiments as well as in a real-life insurance case study. A notable feature for both our simulation experiment and the real-life case study is a comparatively low signal-to-noise ratio, which is a feature common in actuarial applications. We find that the GLMMNet often outperforms or at least performs comparably with an entity-embedded neural network in these settings, while providing the additional benefit of transparency, which is particularly valuable in practical applications.

Importantly, while our model was motivated by actuarial applications, it can have wider applicability. The GLMMNet would suit any applications that involve high-cardinality categorical variables and where the response cannot be sufficiently modelled by a Gaussian distribution, especially where the inherent noisiness of the data is relatively high.

The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, that is of compound Poisson type, are not consistent with Mack’s distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g., number of contracts), we show that the chain ladder predictor and Mack’s estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack’s estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.

A comparison of the performances of pension products that ignores long-term trends might significantly overestimate the long-term impact of volatility risks while underestimating the impact of persistent, low-frequency trends. This paper proposes a comparison making use of projection models based on the long-term risk–return tradeoff proposed by Campbell and Viceira (2005) to explicitly take into account slow-moving economic trends. In order to illustrate the approach and its implications, we discuss the capital protection provided by life-cycle target-date fund strategies and minimum guarantee strategies.

Mortality shocks such as the one induced by the COVID-19 pandemic have substantial impact on mortality models. We describe how to deal with them in the period effect of the Lee–Carter model. The main idea is to not rely on the usual normal distribution assumption as it is not always justified. We consider a mixture distribution model based on the peaks-over-threshold method, a jump model, and a regime switching model and introduce a modified calibration procedure to account for the fact that varying amounts of data are necessary for calibrating different parts of these models. We perform an extensive empirical study for nine European countries, comparing the models with respect to their parameters, quality of fit, and forecasting performance. Moreover, we define five exemplary scenarios regarding the future development of pandemic-related mortality. As a result of our evaluations, we recommend the peaks-over-threshold approach for applications with a possibility of extreme mortality events.

In this contribution, we exploit machine learning techniques to evaluate whether and how close firms are to become successful exporters. First, we train various algorithms using financial information on both exporters and non-exporters in France in 2010–2018. Thus, we show that it is possible to predict the distance non-exporters are from export status. In particular, we find that a Bayesian Additive Regression Tree with Missingness In Attributes (BART-MIA) performs better than other techniques with an accuracy of up to 0.90. Predictions are robust to changes in definitions of exporters and in the presence of discontinuous exporting activity. Eventually, we discuss how our exporting scores can be helpful for trade promotion, trade credit, and assessing aggregate trade potential. For example, back-of-the-envelope estimates show that a representative firm with just below-average exporting scores needs up to 44% more cash resources and up to 2.5 times more capital to get to foreign markets.

This research investigates the role of public sector innovation outcomes, e.g. trademark innovation, information and communication technology (ICT), renewable energy, and governance, in the sustainable development of Bangladesh during 1980–2019. Utilising the dynamic autoregressive distributed lag (DARDL) simulation approach, this study divulges a favourable long-term influencing profile of public sector innovation outcomes, i.e. trademark innovation, ICT, and renewable energy on sustainable development, while governance has a heterogeneous impact. Besides, the findings from the DARDL simulations area plots display 10% counterfactual shocks to the public sector innovation outcomes on sustainable development. Furthermore, the Kernel-based regularised least square machine learning algorithm approach used in the study examines the marginal effects of the public sector innovation outcomes on sustainable development for robust findings. Therefore, the policy suggestions are solely concerned with the public sector’s adoption of more innovation dynamics through appropriate policy formulation.

Longevity risk is putting more and more financial pressure on governments and pension plans worldwide due to pensioners’ increasing trend of life expectancy and the growing numbers of people reaching retirement age. Lee and Carter (1992, Journal of the American Statistical Association, 87(419), 659–671.) applied a one-factor dynamic factor model to forecast the trend of mortality improvement, and the model has since become the field’s workhorse. It is, however, well known that their model is subject to the limitation of overlooking cross-dependence between different age groups. We introduce Factor-Augmented Vector Autoregressive (FAVAR) models to the mortality modelling literature. The model, obtained by adding an unobserved factor process to a Vector Autoregressive (VAR) process, nests VAR and Lee–Carter models as special cases and inherits both frameworks’ advantages. A Bayesian estimation approach, adapted from the Minnesota prior, is proposed. The empirical application to the US and French mortality data demonstrates our proposed method’s efficacy in both in-sample and out-of-sample performance.

Modeling and forecasting of mortality rates are closely related to a wide range of actuarial practices, such as the designing of pension schemes. To improve the forecasting accuracy, age coherence is incorporated in many recent mortality models, which suggests that the long-term forecasts will not diverge infinitely among age groups. Despite their usefulness, misspecification is likely to occur for individual mortality models when applied in empirical studies. The reliableness and accuracy of forecast rates are therefore negatively affected. In this study, an ensemble averaging or model averaging (MA) approach is proposed, which adopts age-specific weights and asymptotically achieves age coherence in mortality forecasting. The ensemble space contains both newly developed age-coherent and classic age-incoherent models to achieve the diversity. To realize the asymptotic age coherence, consider parameter errors, and avoid overfitting, the proposed method minimizes the variance of out-of-sample forecasting errors, with a uniquely designed coherent penalty and smoothness penalty. Our empirical data set include ten European countries with mortality rates of 0–100 age groups and spanning 1950–2016. The outstanding performance of MA is presented using the empirical sample for mortality forecasting. This finding robustly holds in a range of sensitivity analyses. A case study based on the Italian population is finally conducted to demonstrate the improved forecasting efficiency of MA and the validity of the proposed estimation of weights, as well as its usefulness in actuarial applications such as the annuity pricing.

In this paper, we first introduce a simulator of cases estimates of incurred losses called SPLICE (Synthetic Paid Loss and Incurred Cost Experience). In three modules, case estimates are simulated in continuous time, and a record is output for each individual claim. Revisions for the case estimates are also simulated as a sequence over the lifetime of the claim in a number of different situations. Furthermore, some dependencies in relation to case estimates of incurred losses are incorporated, particularly recognising certain properties of case estimates that are found in practice. For example, the magnitude of revisions depends on ultimate claim size, as does the distribution of the revisions over time. Some of these revisions occur in response to occurrence of claim payments, and so SPLICE requires input of simulated per-claim payment histories. The claim data can be summarised by accident and payment “periods” whose duration is an arbitrary choice (e.g. month, quarter, etc.) available to the user. SPLICE is built on an existing simulator of individual claim experience called SynthETIC (introduced in Avanzi et al. 2021b, Insurance: Mathematics and Economics, 100, 296–308), which offers flexible modelling of occurrence, notification, as well as the timing and magnitude of individual partial payments. This is in contrast with the incurred losses, which constitute the additional contribution of SPLICE. The inclusion of incurred loss estimates provides a facility that almost no other simulators do. SPLICE is is a fully documented R package that is publicly available and open source (on CRAN). SPLICE, combined with SynthETIC, provides 11 modules (occurrence, notification, etc.), any one or more of which may be re-designed according to the user’s requirements. It comes with a default version that is loosely calibrated to resemble a specific (but anonymous) Auto Bodily Injury portfolio, as well as data generation functionality that outputs alternative data sets under a range of hypothetical scenarios differing in complexity. The general structure is suitable for most lines of business, with some reparameterisation.

The Lee–Carter model has become a benchmark in stochastic mortality modeling. However, its forecasting performance can be significantly improved upon by modern machine learning techniques. We propose a convolutional neural network (NN) architecture for mortality rate forecasting, empirically compare this model as well as other NN models to the Lee–Carter model and find that lower forecast errors are achievable for many countries in the Human Mortality Database. We provide details on the errors and forecasts of our model to make it more understandable and, thus, more trustworthy. As NN by default only yield point estimates, previous works applying them to mortality modeling have not investigated prediction uncertainty. We address this gap in the literature by implementing a bootstrapping-based technique and demonstrate that it yields highly reliable prediction intervals for our NN model.

This study scrutinizes spatial econometric models and specifications of crop yield response functions to provide a robust evaluation of empirical alternatives available to researchers. We specify 14 competing panel regression models of crop yield response to weather and site characteristics. Using county corn yields in the US, this study implements in-sample, out-of-sample, and bootstrapped out-of-sample prediction performance comparisons. Descriptive propositions and empirical results demonstrate the importance of spatial correlation and empirically support the fixed effects model with spatially dependent error structures. This study also emphasizes the importance of extensive model specification testing and evaluation of selection criteria for prediction.

Innon-life insurance, the payment history can be predictive of the timing of a settlement for individual claims. Ignoring the association between the payment process and the settlement process could bias the prediction of outstanding payments. To address this issue, we introduce into the literature of micro-level loss reserving a joint modeling framework that incorporates longitudinal payments of a claim into the intensity process of claim settlement. We discuss statistical inference and focus on the prediction aspects of the model. We demonstrate applications of the proposed model in the reserving practice with a detailed empirical analysis using data from a property insurance provider. The prediction results from an out-of-sample validation show that the joint model framework outperforms existing reserving models that ignore the payment–settlement association.

Modeling policyholders’ lapse behaviors is important to a life insurer, since lapses affect pricing, reserving, profitability, liquidity, risk management, and the solvency of the insurer. In this paper, we apply two machine learning methods to lapse modeling. Then, we evaluate the performance of these two methods along with two popular statistical methods by means of statistical accuracy and profitability measure. Moreover, we adopt an innovative point of view on the lapse prediction problem that comes from churn management. We transform the classification problem into a regression question and then perform optimization, which is new to lapse risk management. We apply the aforementioned four methods to a large real-world insurance dataset. The results show that Extreme Gradient Boosting (XGBoost) and support vector machine outperform logistic regression (LR) and classification and regression tree with respect to statistic accuracy, while LR performs as well as XGBoost in terms of retention gains. This highlights the importance of a proper validation metric when comparing different methods. The optimization after the transformation brings out significant and consistent increases in economic gains. Therefore, the insurer should conduct optimization on its economic objective to achieve optimal lapse management.

We propose a new neighbouring prediction model for mortality forecasting. For each mortality rate at age x in year t, mx,t, we construct an image of neighbourhood mortality data around mx,t, that is, Ꜫmx,t (x1, x2, s), which includes mortality information for ages in [x-x1, x+x2], lagging k years (1 ≤ k ≤ s). Combined with the deep learning model – convolutional neural network, this framework is able to capture the intricate nonlinear structure in the mortality data: the neighbourhood effect, which can go beyond the directions of period, age, and cohort as in classic mortality models. By performing an extensive empirical analysis on all the 41 countries and regions in the Human Mortality Database, we find that the proposed models achieve superior forecasting performance. This framework can be further enhanced to capture the patterns and interactions between multiple populations.

Based on evidence gathered from a newly built large macroeconomic dataset (MD) for the UK, labelled UK-MD and comparable to similar datasets for the United States and Canada, it seems the most promising avenue for forecasting during the pandemic is to allow for general forms of nonlinearity by using machine learning (ML) methods. But not all nonlinear ML methods are alike. For instance, some do not allow to extrapolate (like regular trees and forests) and some do (when complemented with linear dynamic components). This and other crucial aspects of ML-based forecasting in unprecedented times are studied in an extensive pseudo-out-of-sample exercise.

Nowcasting, that is, forecasting the current economic conditions, is a key ingredient for decision making, but it is complex, even more so for a small open economy, due to the higher volatility of its GDP. In this paper, we review the required steps, taking Luxembourg as an example. We consider both standard and alternative indicators, used as inputs in several nowcasting methods, including various factor and machine learning models. Overall, mixed frequency dynamic factor models and neural networks perform well, both in absolute terms and in relative terms with respect to a benchmark autoregressive model. The gains are larger during problematic times, such as the financial crisis and the recent Covid period.

The Covid-19 pandemic has put forecasting under the spotlight, pitting epidemiological models against extrapolative time-series devices. We have been producing real-time short-term forecasts of confirmed cases and deaths using robust statistical models since 20 March 2020. The forecasts are adaptive to abrupt structural change, a major feature of the pandemic data due to data measurement errors, definitional and testing changes, policy interventions, technological advances and rapidly changing trends. The pandemic has also led to abrupt structural change in macroeconomic outcomes. Using the same methods, we forecast aggregate UK unemployment over the pandemic. The forecasts rapidly adapt to the employment policies implemented when the UK entered the first lockdown. The difference between our statistical and theory based forecasts provides a measure of the effect of furlough policies on stabilising unemployment, establishing useful scenarios had furlough policies not been implemented.