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.

Using telematics technology, insurers are able to capture a wide range of data to better decode driver behavior, such as distance traveled and how drivers brake, accelerate, or make turns. Such additional information also helps insurers improve risk assessments for usage-based insurance, a recent industry innovation. In this article, we explore the integration of telematics information into a classification model to determine driver heterogeneity. For motor insurance during a policy year, we typically observe a large proportion of drivers with zero accidents, a lower proportion with exactly one accident, and a far lower proportion with two or more accidents. We here introduce a cost-sensitive multi-class adaptive boosting (AdaBoost) algorithm we call SAMME.C2 to handle such class imbalances. We calibrate the algorithm using empirical data collected from a telematics program in Canada and demonstrate an improved assessment of driving behavior using telematics compared with traditional risk variables. Using suitable performance metrics, we show that our algorithm outperforms other learning models designed to handle class imbalances.

Catastrophe insurance markets fail to provide sufficient protections against natural catastrophes, whereas they have the capacity to absorb the losses. In this paper, we assume the catastrophic risks are dependent and extremely heavy-tailed, and insurers have limited liability to cover losses up to a certain amount. We provide a comprehensive study to show that the diversification in the catastrophe insurance markets can be transited from suboptimal to preferred by increasing the number of insurers in the market. This highlights the importance of coordination among insurers and the government intervention in encouraging insurers to participate in the catastrophe insurance market to exploit risk sharing. Simulation studies are provided to illuminate the key findings of our results.

This article proposes a complex economic scenario generator that nests versions of well-known actuarial frameworks. The generator estimation relies on the Bayesian paradigm and accounts for both model and parameter uncertainty via Markov chain Monte Carlo methods. So, to the question is less more?, we answer maybe, but it depends on your criteria. From an in-sample fit perspective, on the one hand, a complex economic scenario generator seems better. From the conservatism, forecasting and coverage perspectives, on the other hand, the situation is less clear: having more complex models for the short rate, term structure and stock index returns is clearly beneficial. However, that is not the case for inflation and the dividend yield.

In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.

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.

Target benefit (TB) plans that incorporate intergenerational risk sharing have been demonstrated to be welfare improving over the long term. However, there has been little discussion of the short-term benefits for members in a defined benefit (DB) plan that is transitioning to TB. In this paper, we adopt a two-step approach that is designed to ensure the long-term sustainability of the new plan, without unduly sacrificing the benefit security of current retirees. We propose a cohort-based transition plan for reducing intergenerational inequity. Our study is based on simulations using an economic scenario generator with some theoretical results under simplified settings.

We extend the Annually Recalculated Virtual Annuity (ARVA) spending rule for retirement savings decumulation (Waring and Siegel (2015) Financial Analysts Journal, 71(1), 91–107) to include a cap and a floor on withdrawals. With a minimum withdrawal constraint, the ARVA strategy runs the risk of depleting the investment portfolio. We determine the dynamic asset allocation strategy which maximizes a weighted combination of expected total withdrawals (EW) and expected shortfall (ES), defined as the average of the worst 5% of the outcomes of real terminal wealth. We compare the performance of our dynamic strategy to simpler alternatives which maintain constant asset allocation weights over time accompanied by either our same modified ARVA spending rule or withdrawals that are constant over time in real terms. Tests are carried out using both a parametric model of historical asset returns as well as bootstrap resampling of historical data. Consistent with previous literature that has used different measures of reward and risk than EW and ES, we find that allowing some variability in withdrawals leads to large improvements in efficiency. However, unlike the prior literature, we also demonstrate that further significant enhancements are possible through incorporating a dynamic asset allocation strategy rather than simply keeping asset allocation weights constant throughout retirement.