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Arguably the most important developments in the insurance industry in the last decade have been centered around two themes: regulation and machine learning. Regulation has affected both actuarial work and research in insurance mathematics through the introduction of Solvency II in 2016, and more recently IFRS 17. The use of machine learning methods, and in particular neural network models and tree-based methods, has been increasing in research papers in insurance mathematics in recent years, and has furthermore started influencing the insurance industry, e.g. in pricing. This thesis consists of four papers exploring these two themes. Paper I is focused on how to implement the new accounting regulation IFRS 17 in an economically and theoretically sound way. We provide a mathematical interpretation of this extensive regulation. In particular we define an algorithm for how to determine unearned future profits, and how these can be systematically converted to actual profits over time. The algorithm is a crucial ingredient in any practical implementation of the regulation. Furthermore, we suggest suitable methods for valuation of insurance contracts, and allocation of this value to groups of contracts, and demonstrate the practicability of the algorithm and methods in a large scale numerical example. Paper II is concerned with mortality forecasting, which is an important aspect of valuing and pricing life insurance contracts. We consider an extension of the Poisson Lee-Carter model, where the mortality trend is modelled by a long short-term memory (LSTM) neural network. Different calibration approaches of the network are suggested, with the aim of using training data efficiently. In particular, we consider a novel approach to splitting data into training and validation data based on the construction of synthetic subpopulations. The stability of long-term predictions is improved by considering boosted versions of the model, which allows us to obtain reasonable prediction

We consider a premium control problem in discrete time, formulated in terms of a Markov decision process. In a simplified setting, the optimal premium rule can be derived with dynamic programming methods. However, these classical methods are not feasible in a more realistic setting due to the dimension of the state space and lack of explicit expressions for transition probabilities. We explore reinforcement learning techniques, using function approximation, to solve the premium control problem for realistic stochastic models. We illustrate the appropriateness of the approximate optimal premium rule compared with the true optimal premium rule in a simplified setting and further demonstrate that the approximate optimal premium rule outperforms benchmark rules in more realistic settings where classical approaches fail.

We consider a simple long short-term memory (LSTM) neural network extension of the Poisson Lee-Carter model, with a particular focus on different procedures for how to use training data efficiently, combined with ensembling to stabilise the predictive performance. We compare the standard approach of withholding the last fraction of observations for validation, with two other approaches: sampling a fraction of observations randomly in time; and splitting the population into two parts by sampling individual life histories. We provide empirical and theoretical support for using these alternative approaches. Furthermore, to improve the stability of long-term predictions, we consider boosted versions of the Poisson Lee-Carter LSTM. In the numerical illustrations it is seen that even in situations where mortality rates are essentially log-linear as a function of calendar time, the boosted model does not perform significantly worse than a simple random walk with drift, and when non-linearities are present the predictive performance is improved. Moreover, boosting allows us to obtain reasonable model calibrations based on as few data points as 20 years.

The general principles for determining the financial performance of a company is that revenue is earned as goods are delivered or services provided, and that expenses in the period are made up of the costs associated with this earned revenue. In the insurance industry, premium payments are typically made upfront, and can provide coverage for several years, or be paid many years before the coverage period starts. The associated costs are often not fully known until many years later. Hence, complexity arises both in determining how a premium paid should be earned over time, and in valuing the costs associated with this earned premium. IFRS 17 attempts to align the insurance industry with these general accounting principles. We bring this new accounting standard into the realm of actuarial science, through a mathematical interpretation of the regulatory texts, and by defining the algorithm for profit or loss in accordance with the new standard. Furthermore, we suggest a computationally efficient risk-based method of valuing a portfolio of insurance contracts and an allocation of this value to subportfolios. Finally, we demonstrate the practicability of these methods and the algorithm for profit or loss in a large-scale numerical example.

The papers presented here cover two different themes, both with applications in life insurance. The focus in the first paper is on determining the financial position and performance of an insurance company, in a accordance with IFRS 17. To derive the financial performance of an insurance company one needs to determine how a premium paid should be earned over time, and how to measure the costs associated with this earned premium. This is a complex matter, since premium payments can provide many years of coverage, and claims payments often are not fully known until many years later. IFRS 17 suggests a way of doing this, by specifying how to measure the unearned future profit for a group of insurance contracts. We give a mathematical interpretation of the regulatory texts, resulting in an algorithm for profit or loss defined in terms of the change in this unearned future profit and the risk-based liability value. Furthermore, we suggest a multi-period cost-of-capital approach as an appropriate valuation method for this purpose, and illustrate the practicability of this method, and allocation of this value to subportfolios, in a large scale numerical example. The second paper concentrates on mortality forecasting, which is an important aspect of valuing and pricing life insurance contracts. We consider an extension of the Poisson Lee-Carter model, where the mortality trend is modelled by a long short-term memory neural network. Different calibration approaches of the network are suggested, with the aim of using training data efficiently, combined with ensembling to enhance the predictive performance. The stability of long-term predictions is improved by considering boosted versions of the model, which, furthermore, allows us to obtain reasonable predictions even for cases when data is very scarce.