The time-series nature of mortality rates lends itself to processing through neural networks that are specialized to deal with sequential data, such as recurrent and convolutional networks. The aim of this work is to show how the structure of the Lee–Carter model can be generalized using a relatively simple shallow convolutional network model, allowing for its components to be evaluated in familiar terms. Although deep networks have been applied successfully in many areas, we find that deep networks do not lead to an enhanced predictive performance in our approach for mortality forecasting, compared to the proposed shallow one. Our model produces highly accurate forecasts on the Human Mortality Database, and, without further modification, generalizes well to the United States Mortality Database.

We define the nagging predictor, which, instead of using bootstrapping to produce a series of i.i.d. predictors, exploits the randomness of neural network calibrations to provide a more stable and accurate predictor than is available from a single neural network run. Convergence results for the family of Tweedie’s compound Poisson models, which are usually used for general insurance pricing, are provided. In the context of a French motor third-party liability insurance example, the nagging predictor achieves stability at portfolio level after about 20 runs. At an insurance policy level, we show that for some policies up to 400 neural network runs are required to achieve stability. Since working with 400 neural networks is impractical, we calibrate two meta models to the nagging predictor, one unweighted, and one using the coefficient of variation of the nagging predictor as a weight, finding that these latter meta networks can approximate the nagging predictor well, only with a small loss of accuracy.

Rapid advances in artificial intelligence (AI) and machine learning are creating products and services with the potential not only to change the environment in which actuaries operate, but also to provide new opportunities within actuarial science. These advances are based on a modern approach to designing, fitting and applying neural networks, generally referred to as “Deep Learning”. This paper investigates how actuarial science may adapt and evolve in the coming years to incorporate these new techniques and methodologies. Part 1 of this paper provides background on machine learning and deep learning, as well as an heuristic for where actuaries might benefit from applying these techniques. Part 2 of the paper then surveys emerging applications of AI in actuarial science, with examples from mortality modelling, claims reserving, non-life pricing and telematics. For some of the examples, code has been provided on GitHub so that the interested reader can experiment with these techniques for themselves. Part 2 concludes with an outlook on the potential for actuaries to integrate deep learning into their activities. Finally, a supplementary appendix discusses further resources providing more in-depth background on machine learning and deep learning.

Rapid advances in artificial intelligence (AI) and machine learning are creating products and services with the potential not only to change the environment in which actuaries operate but also to provide new opportunities within actuarial science. These advances are based on a modern approach to designing, fitting and applying neural networks, generally referred to as “Deep Learning.” This paper investigates how actuarial science may adapt and evolve in the coming years to incorporate these new techniques and methodologies. Part 1 of this paper provides background on machine learning and deep learning, as well as an heuristic for where actuaries might benefit from applying these techniques. Part 2 of the paper then surveys emerging applications of AI in actuarial science, with examples from mortality modelling, claims reserving, non-life pricing and telematics. For some of the examples, code has been provided on GitHub so that the interested reader can experiment with these techniques for themselves. Part 2 concludes with an outlook on the potential for actuaries to integrate deep learning into their activities. Finally, a supplementary appendix discusses further resources providing more in-depth background on machine learning and deep learning.

A vast and growing literature on explaining deep learning models has emerged. This paper contributes to that literature by introducing a global gradient-based model-agnostic method, which we call Marginal Attribution by Conditioning on Quantiles (MACQ). Our approach is based on analyzing the marginal attribution of predictions (outputs) to individual features (inputs). Specifically, we consider variable importance by fixing (global) output levels, and explaining how features marginally contribute to these fixed global output levels. MACQ can be seen as a marginal attribution counterpart to approaches such as accumulated local effects, which study the sensitivities of outputs by perturbing inputs. Furthermore, MACQ allows us to separate marginal attribution of individual features from interaction effects and to visualize the 3-way relationship between marginal attribution, output level, and feature value.