Learning from historical and recent evolutions in mortality rates and life expectancy is key to produce realistic scenarios for future mortality rates, necessary for the valuation of the liabilities of life insurance companies and pension funds. The 2024 edition of the Summer School of the Swiss Association of Actuaries will focus on actuarial, statistical and machine learning tools to model mortality data, and the use of the constructed models for the valuation and management of life contingent risks.  

The Summer School will kick off with an introductory, motivational lecture and discussion that sets the scene for the technical tools that will be studied during the week. This lecture will provide an overview of  the exposure of European insurance companies and pension funds to longevity risk and some of the most notable recent transactions in an attempt to hedge this risk (e.g., Aegon reinsuring the longevity exposure of  Dutch pension insurance contracts with Reinsurance Group of America, end of 2021). Moreover, the lecture will sketch key points in the ongoing debates on the sustainability of pension systems, illustrated a.o. with the upcoming change in the Dutch second pillar from a collective system with defined benefits to a collective defined contribution scheme.

Participants will explore the construction and calibration of stochastic multi-population mortality models from annual, all-cause, population-level death counts and exposures.  We cover the state-of-the-art literature and discuss the essentials of the stochastic multi-population mortality model developed (and maintained) by the Royal Dutch Actuarial Association. This model was developed via a unique partnership between industry and academia and elegantly combines insights from the evolution in mortality rates in a set of European countries on the one hand and the mortality statistics of the country of interest (e.g., the Netherlands) on the other hand. The use of the constructed model as a generator of scenarios for future mortality rates will be demonstrated. Relying on our first-hand experience, we will also cover related topics such as the biennial updates of the model, its impact on industry and the response to modeling challenges such as the COVID-19 shock.

Next, participants will explore data handling and exploration tools as well as statistical and machine learning methods to unravel insights from more granular mortality data. The analysis of cause-specific mortality rates will extend our initial focus on all-cause mortality data. Modelling mortality rates for a book of insureds in the presence of covariates or risk factors allows to go beyond the initial set-up of population-level mortality data. Instead of working with annual data, we will also explore more fine-grained time scales (daily, weekly) and the relation between high-resolution gridded data sets on climate and environmental variables and mortality statistics at a regional level.  

The lectures will be supplemented by several practical sessions where the participants will apply the learned statistical techniques to mortality datasets using the R software environment. A dedicated GitHub repo and landing page with the course material (including data, scripts, background reading material and lecture sheets) will be shared with the participants.

Throughout the Summer School, the following topics will be considered:

  • basics of mortality modelling and demographics, including useful data visuals
  • single and multi-population stochastic mortality models: set-up, calibration, scenario generation; this includes the essentials of (e.g.) Lee-Carter, Li-Lee, Cairns-Blake-Dowd models and the use of time series models to project mortality rates
  • the valuation of life contingent risks, reflections on longevity and mortality risk, the design of shock scenarios and the quantification of their impact; the design and valuation of instruments recently used to hedge longevity risk
  • data handling tools, illustrated with mortality data collected at different levels of granularity (e.g., annual but also weekly, daily, population but also portfolio and regional, all-cause but also cause-specific)
  • a range of statistical and machine learning methods for the analysis of mortality rates.

Upon completion of the course the participants will:

  • understand and master the essentials of stochastic mortality models, and have acquired insights into basic time series models, statistical and machine learning methods for count and survival data
  • be able to apply these for the valuation of life contingent risks and the quantification of longevity risk
  • be able to reflect on modelling challenges associated with longevity, the pros and cons of the use of different modelling strategies in this context
  • have a basic understanding of suitable tools and packages for data handling and analysis of mortality data in R.

Required prerequisites are an intermediate-level knowledge of probability and statistics, actuarial mathematics and basic programming skills.