Ronald Richman

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. Although appealing intuitively, a naive implementation of these networks does
not lead to enhanced predictive performance. We show how the structure of the Lee Carter
model can be generalized, and propose a relatively simple convolutional network model that
can be interpreted as a… Show more

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. Although appealing intuitively, a naive implementation of these networks does
not lead to enhanced predictive performance. We show how the structure of the Lee Carter
model can be generalized, and propose a relatively simple convolutional network model that
can be interpreted as a generalization of the Lee Carter model, allowing for its components
to be evaluated in familiar terms. The model produces highly accurate forecasts on the Human
Mortality Database, and, without further modification, generalizes well to the United
States Mortality Database. Show less

A simple formula for non-discriminatory insurance pricing is introduced. This formula is based on the assumption that certain individual (discriminatory) policyholder information is not allowed to be used for insurance pricing. The suggested procedure can be summarized as follows: First, we construct a price that is based on all available information, including discriminatory information. Thereafter, we average out the effect of discriminatory information. This averaging out is done such that… Show more

A simple formula for non-discriminatory insurance pricing is introduced. This formula is based on the assumption that certain individual (discriminatory) policyholder information is not allowed to be used for insurance pricing. The suggested procedure can be summarized as follows: First, we construct a price that is based on all available information, including discriminatory information. Thereafter, we average out the effect of discriminatory information. This averaging out is done such that discriminatory information can also not be inferred from the remaining non-discriminatory one, thus, neither allowing for direct nor for indirect discrimination. Show less

Deep Learning models are currently being introduced into business processes to support decision-making in insurance companies. At the same time model risk is recognized as an increasingly relevant field within the management of operational risk that tries to mitigate the risk of poor business decisions because of flawed models or inappropriate model use. In this paper we try to determine how Deep Learning models are different from established actuarial models currently in use in insurance… Show more

Deep Learning models are currently being introduced into business processes to support decision-making in insurance companies. At the same time model risk is recognized as an increasingly relevant field within the management of operational risk that tries to mitigate the risk of poor business decisions because of flawed models or inappropriate model use. In this paper we try to determine how Deep Learning models are different from established actuarial models currently in use in insurance companies and how these differences might necessitate changes in the model risk management framework. We analyse operational risk in the development and implementation of Deep Learning models using examples from pricing and mortality forecasting to illustrate specific model risks and controls to mitigate those risks. We discuss changes in model governance and the role that model risk managers could play in providing assurance on the appropriate use of Deep Learning models. Show less

In this tutorial we introduce recurrent neural networks (RNNs), and we describe the two most popular RNN architectures. These are the long short-term memory (LSTM) network and gated recurrent unit (GRU) network. Their common field of application is time series modeling, and we demonstrate their use on a mortality rate prediction problem using data from the Swiss female and male populations.

The Lee-Carter model is a basic approach to forecasting mortality rates of a single population. Although extensions of the Lee-Carter model to forecasting rates for multiple populations have recently been proposed, the structure of these extended models is hard to justify and the models are often difficult to calibrate, relying on customized optimization schemes. Based on the paradigm of representation learning, we extend the Lee-Carter model to multiple populations using neural networks, which… Show more

The Lee-Carter model is a basic approach to forecasting mortality rates of a single population. Although extensions of the Lee-Carter model to forecasting rates for multiple populations have recently been proposed, the structure of these extended models is hard to justify and the models are often difficult to calibrate, relying on customized optimization schemes. Based on the paradigm of representation learning, we extend the Lee-Carter model to multiple populations using neural networks, which automatically select an optimal model structure. We fit this model to mortality rates since 1950 for all countries in the Human Mortality Database and observe that the out-of-sample forecasting performance of the model is highly competitive. Show less

The main idea of this paper is to embed a classical actuarial regression model into a neural network architecture. This nesting allows us to learn model structure beyond the classical actuarial regression model if we use as starting point of the neural network calibration exactly the classical actuarial model. Such models can be fitted efficiently which allows us to explore bootstrap methods for prediction uncertainty. As an explicit example we consider the cross-classified over-dispersed… Show more

The main idea of this paper is to embed a classical actuarial regression model into a neural network architecture. This nesting allows us to learn model structure beyond the classical actuarial regression model if we use as starting point of the neural network calibration exactly the classical actuarial model. Such models can be fitted efficiently which allows us to explore bootstrap methods for prediction uncertainty. As an explicit example we consider the cross-classified over-dispersed Poisson model for general insurance claims reserving. We demonstrate how this model can be improved by neural network features. Show less

Rapid advances in Artificial Intelligence 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… Show more

Rapid advances in Artificial Intelligence 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. After providing some background on machine learning and deep learning, and providing a heuristic for where actuaries might benefit from applying these techniques, the paper 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. The paper concludes with an outlook on the potential for actuaries to integrate deep learning into their activities. Show less

Actuaries rely on population mortality rates to determine compensation in cases of damages,
trends in mortality rates inform the modelling of mortality risk and valuation of insurance
companies and pension schemes and, not least, actuarial calculations of population mortality
contribute to wider societal debates. Estimating the level and trend in population mortality rates
at advanced ages in South Africa is complicated by potential problems. Population and death
data… Show more

Actuaries rely on population mortality rates to determine compensation in cases of damages,
trends in mortality rates inform the modelling of mortality risk and valuation of insurance
companies and pension schemes and, not least, actuarial calculations of population mortality
contribute to wider societal debates. Estimating the level and trend in population mortality rates
at advanced ages in South Africa is complicated by potential problems. Population and death
data, particularly in developing countries, often suffer from age misreporting – age exaggeration
and digit preference. In addition, censuses may under- or overestimate the population and
registration of deaths is usually incomplete in developing countries
In this research, we use the Death Distribution Methods (Moultrie et al., 2013) to correct
the death data for incomplete registration of deaths, and the Near Extinct Generation (NEG)
methods (Thatcher et al., 2002) to estimate the population by projecting future deaths of nearly
extinct cohorts. In applying NEG methods to the South African data, we exploit the theoretical
connection to actuarial methods for the calculation of claims incurred but not yet reported,
and propose an adapted NEG method based on the chain-ladder model of Renshaw and Verrall
(1998) to smooth the digit preference in the death data. We use this model to re-estimate the
population at each age from 70 and above and to calculate mortality rates since 1996. We find
that both the population and death data suffer from the same pattern of digit preference and that the population data are affected by age exaggeration, leading to underestimated mortality rates if the census counts are used as exposures. The level and trend in mortality rates are discussed and compared to the mortality rates in the Human Mortality Database, other studies of South African mortality and insured life tables.

The paper was "Highly Commended" by the Awards Committee of the IFoA in 2017. Show less