Combining Actuarial and Behavioural Perspectives to the Understanding of Longevity Risk

A new perspective on longevity risk perception

Statistical models based on actuarial data are used to project longevity, yet as individuals we often use heuristics when asked to consider our own longevity. We spoke to Professor Enrico De Giorgi and Dr Giovanna Apicella about how they’re combining behavioural and actuarial insights to bring a fresh perspective to how we perceive longevity risk.

An annuity appears to be an

attractive option for individuals planning their retirement, providing people with a guaranteed income for the rest of their lives rather than the uncertainty associated with managing their own money. However, despite the benefits widely associated with annuities, the market for individual life annuities is fairly small in the US, UK and many other developed countries, part of what has been termed the annuity puzzle. “Very few individuals buy private annuities, the market is not that big,” says Enrico De Giorgi, Professor of Mathematics at the University of St.Gallen. Together with his colleague Dr Giovanna Apicella, Professor De Giorgi has looked into data from the Health and Retirement Study (HRS) and SHARE to gain some fresh insights on why people might choose not to buy annuities. “When we looked at the data we discovered that there was a marked disparity between people’s subjective beliefs about their own survival prospects, relative to their actuarial probability of surviving,” he continues.

This could be an important factor in why many people decide not buy an annuity. The data shows that young people significantly under-estimate their own longevity, and then when people get to the age of 75 or even older, they may find that annuities are too expensive. “It may prove hard to buy an

annuity at that stage, despite the fact that rates are higher” explains Professor De Giorgi. As the Principal Investigator of a new research project, Professor De Giorgi aims to shed new light on the subjective beliefs which influence our decisions in this area, work which holds important implications in the context of our aging society and the need to fund care for high numbers of elderly people. “The private insurance market will become more and more important in financing retirement,” he outlines. “The cost of conventional pension systems is becoming very, very high, precisely because people are living for longer. Giovanna has a very good knowledge of these issues from an actuarial point of view, while I come more from a behavioural perspective.”

It’s important that people save their money into private pension plans, so that they can have the same quality of life when they retire as they did when they were younger. We want to understand why many people are not currently willing to do this.

Behavioural insights

The aim in the project is to bring a fresh perspective to the available data by combining these two viewpoints. This involves looking into the underlying reasons why younger people initially under-estimate their own longevity, while generally older people have a tendency to over-estimate it, often using heuristics. “Heuristics are a mental tool we use to estimate probabilities,”

says Professor De Giorgi. While heuristics work well in many contexts, in terms of judging individual longevity they can lead to assessments that are quite different to those derived from probability theory, which is where behavioural economics enters the picture. “Our conjecture is that people tend to react to health shocks. So when people get a shock – even something simple, like the flu – they tend to over-react. This overreaction leads to an update of beliefs, which is much stronger than what the data tells us about the actuarial probabilities,” explains Professor De Giorgi.

This conjecture suggests that people tend to over-react to health shocks, which leads to this pattern of survival beliefs that has been observed in younger and older people. Researchers in the project are now looking to assess the evolution of subjective beliefs about longevity empirically against the objective pattern, as shown by the data. “A more objective pattern for survival probabilities is generated by actuarial models. We use mathematical and statistical methods to generate future patterns of longevity for the people included in our sample,” says Dr Apicella. The data being used in the project relates to a section of the US population over the period between 1996 and 2016. “It is a very comprehensive, well-known database,” continues Dr Apicella. “It includes a lot of modules that concern several domains of life, for instance people’s expectations about their longevity, their physical health, and their cognitive abilities.”

The comprehensive nature of the database is an important attribute in terms of investigating the many different factors that may affect individual longevity. By analysing this data on the US population, together with data about the past mortality experience of this population which has been recovered from the Human Mortality Database, Dr Apicella aims to build a deeper picture of the factors behind longevity. “We fit our stochastic mortality (CBD or M5) model to this database, and we obtain the survival probabilities forecasts, representing the actuarial benchmark against which we study subjective expectations, in both their level and dynamics,” she explains. Indeed, researchers have also delved further into the data to investigate how certain groups of people react to health shocks. “In particular, we consider people who are not affected by any of the five main diseases in our study – cancer, diabetes, heart conditions, high blood pressure and emotional disorders,” says Dr Apicella. “We also consider the people who are affected by one of these diseases, or by two or more simultaneously.”

Researchers know how the actuarial probability associated to a person with a specific health condition declines over time, yet it has also been found that the subjective probability about their own longevity that these people express evolves differently for some categories of individuals. This suggests that people could be driven by some mis-perceptions, by heuristics, when they express their beliefs about their survival prospects. “They do not correctly weigh statistical information about a health-related event when they formulate their beliefs. If they did, then their subjective survival probabilities would decline by a larger degree when they are diagnosed with a serious disease than a less severe one, as reflected by actuarial models,” outlines Dr Apicella. “Since this does not happen, there must be something different that drives people’s perceptions.”

An individual’s emotional perspective is a major factor here, as a generally optimistic person may adopt the same outlook when considering their own health, which can vary according to age. Evidence shows that people in different age groups are characterised by different levels of life satisfaction. “Life satisfaction can be represented graphically as a U-shaped curve, with a nadir reached in middle age, around the age of 50,” explains

Combining Actuarial and Behavioural Perspectives to the Understanding of Longevity Risk Project Objectives

The project’s objectives are: (i) document if and how subjective and actuarial probabilities differ, (iii) understand how individuals form their beliefs on survival and whether these beliefs are biased or also reveal private information useful for the pricing of insurance products; (iv) understand how the demand for insurance products depend on subjective beliefs on survival probabilities; (v) improve the design of life insurance products accounting for subjective beliefs.

Project Funding

The project is financially supported by the Swiss National Science Foundation with 237’370.00 CHF

Contact Details

Professor Enrico De Giorgi University of St.Gallen, MS - Faculty of Mathematics and Statistics, SEPS - School of Economics and Political Science Bodanstrasse 6 9000 St.Gallen, Switzerland T: +41 71 224 24 30 E: enrico.degiorgi@unisg.ch W: www.enricodegiorgi.com

Giovanna Apicella Enrico De Giorgi

Enrico De Giorgi is Full Professor of Mathematics at the University of St. Gallen. He holds an MS in Mathematics from the Swiss Federal Institute of Technology Zurich and a PhD in Economics from the University of Zurich. His research interests are decision theory and behavioural finance, with applications to Portfolio Selection, Asset Pricing, Insurance, etc. Currently, he is Associate Editor of Decisions in Economics and Finance. He also holds Advisory Positions in the FinTech industry and is Founding Partner of BhFS Behavioural Finance Solutions.

Giovanna Apicella is a Postdoctoral Researcher at the University of St. Gallen. She obtained her PhD in Statistical SciencesCurriculum Actuarial Sciences from Sapienza University of Rome. Her research, addressing the longevity risk assessment, currently integrates behavioural perspectives into a solid background on statistical and mathematical methods for mortality modelling and forecasting. Dr Apicella. Older people tend to have higher levels of life satisfaction, which Dr Apicella says is an important consideration in the project’s research. “This state of mind, this attitude, could have implications for how individuals perceive the likelihood of uncertain events, which are by nature random,” she continues. “We use ideas from the behavioural sciences, that are widely used in the financial field, to understand longevity, which is uncertain.”

Individual longevity

The wider backdrop to this research is the evolving demographic picture in European societies, with people living for longer and longer, which raises new questions around healthcare funding. Those of us who want a healthy, happy and prosperous retirement need to plan for it, believes Dr Apicella.

“It’s important that people save their money into private pension plans, so that they can have the same quality of life when they retire as they did when they were younger. Studying subjective beliefs paves the way to an understanding of why many people are not currently willing to do this,” she says. This research also holds wider relevance to actuarial practice, something that Dr Apicella is keen to explore further. “We are looking to make use of the information that can be drawn from these subjective probabilities, in order to enrich probability forecasts from an actuarial point of view,” she explains. “Individuals use a lot of information when they express subjective probabilities about their own longevity.”

Some of this information may be derived from heuristics and based on individual perceptions, so not statistically verified from an actuarial point of view. However, there may also be some other information within these subjective expectations that is relevant in terms of actuarial calculations.

“Some of this information may give us an insight into the genetic background of an individual,” outlines Dr Apicella. By combining actuarial and behavioural insights, Professor De Giorgi and Dr Apicella hope to lay the foundations for improved predictions of longevity. “If you are able to detect biases in information derived from subjective expectations, and to build a relationship between subjective expectations and actuarial probabilities, then you will eventually be able to build a model that takes into account several factors that are currently neglected,” explains Dr Apicella. “That then leads to an improved prediction of longevity from an actuarial point of view.”