Author: Marilyn
Discussion Paper 2602
ADM’s APPLE: The Accelerated Deaths Model with an Application to the Covid-19 Pandemic
Andrew J.G. Cairns, David BlakeAbstract
The Accelerated Deaths Model (ADM) builds on the hypothesis that, within a given age cohort, those who are less healthy are more likely to die if infected with Covid-19 than healthier people, leaving a pool of on-average healthier survivors. We use the term ‘detrimental selection’ which has two complementary aspects: the years of life lost by those who experienced an accelerated death; and the higher average life expectancy of survivors which we call their ‘adjusted post-pandemic life expectancy’ (ADM’s APPLE). Our model represents a novel synthesis of recent advances in our comprehension of mortality heterogeneity and the development of the Proportionality Hypothesis – both of which have improved our understanding of the Covid-19 pandemic. In particular, we identify an important positive relationship between mortality heterogeneity and accelerated deaths. We find, in the case of the Covid-19 pandemic in England, that the years of life lost by those who experienced an accelerated death, while significantly lower than pre-Covid life expectancy, was greater than reported in the media at the time. We also find that the increase in the mean life expectancy of survivors was very small. As a result, the impact on annuity providers (e.g., in terms of potentially higher annuity prices), pension schemes and life insurers was also very small. In contrast, we find that the impact on life expectancy of a general change in future mortality assumptions post-pandemic (i.e., the base mortality table and improvement rate) would be much greater. The ADM has potentially wide application, e.g., to other types of contagion and to climate-related deaths, where we would expect there to be a positive correlation between deaths and all-cause mortality (consistent with the Proportionality Hypothesis), but where the degree of detrimental selection might be different.Discussion Paper 2601
Pension Funds and Sustainability
David BlakeAbstract
This article looks at the problem of climate change and sustainable development solutions to this problem, focusing on the role that pension funds can play in supporting sustainability.Discussion Paper 2504
Mental time travel and the valuation of financial investments: analysing five biases that cause pricing anomalies
David Blake and John PicklesAbstract
Purpose
The purpose of this paper is to analyse five biases in the valuation of financial investments using a mental time travel framework involving thought investments – with no objective time passing.Design/methodology/approach
An investment’s initial value, together with any periodic funding cash-flows, are mentally projected forward (at an expected rate of return) to give the value at the investment horizon; and this projected value is mentally discounted back to the present. If there is a difference between the initial and present values, then this can imply a bias in valuation.Findings
The study identifies (and gives examples of) five real-world valuation biases: biased funding cash-flow estimates (e.g., mega infrastructure projects); biased rate of return projections (e.g., market crises, tech stock carve-outs); biased discount rate estimates (e.g., dual-listed shares, dual-class shares, short-termism, time-risk misperception, and long-termism); time-duration misestimation or perception bias when projecting (e.g., time-contracted projections which lead to short-termism); and time-duration misestimation or perception bias when discounting (e.g., time-extended discounting which also leads to short-termism). More than one bias can be operating at the same time and we give an example of low levels of retirement savings being the result of the biased discounting of biased projections. Finally, we consider the effects of the different biases of different agents operating simultaneously.Originality/value
The paper examines key systematic misestimation and psychological biases underlying financial investment valuation pricing anomalies.Keywords:
financial investment valuation, thought investment, Mental time travel, Rational and irrational expectations, Projecting, Discounting, Biases, Heterogeneous agents.Discussion Paper 2505
The Impact of Covid-19 on Higher-Age Mortality.
Andrew J.G. Cairns, David Blake, Amy R. Kessler and Marsha Kessler.Abstract
We propose a simple model for accelerated deaths that draws on the observation that many of those who died from Covid-19 were often, but not always, much less healthy than the average for their age group; further, the vast majority who died were over the age of 50. The model predicts that, in the absence of additional secondary effects, the impact on the life expectancy of survivors (the anti-selection effect) will be very small, and that the degree of impact depends on the average years of life lost by those who die from Covid-19. The philosophy underpinnning the model is supported by reference to both all-cause mortality by age and all-cause mortality by Socio-economic deprivation group. In combination, these support a proportionality link between Covid-19 mortality and individual frailty or death rates. The Accelerated Deaths Model is consistent with the mortality experience associated with respiratory diseases over the period 2013-15 and with past seasonal influenza epidemics.Keywords:
Covid-19, all-cause mortality, frailty, co-morbidities, deprivation, Accelerated Deaths Model, Proportionality Hypothesis, anti-selection.Discussion Paper 2502
Incorporating Vitagions into Stochastic Longevity Models
Maria Carannante, Valeria D’Amato, Cinzia Di Palo, Maria Sole StaffaAbstract
Assessing mortality dynamics remains a central challenge in demographic, actuarial, and public health research, primarily due to the difficulty of producing reliable forecasts. This complexity is particularly highlighted during periods with large deviations from long-term trends, such as sudden mortality increases due to pandemics or decreases driven by medical and technological breakthroughs. In this context, we address the need for enhanced stochastic models that integrate sudden and significant mortality improvements, termed “vitagions”, into forward looking forecasts. While foundational stochastic mortality models, such as those developed by Cairns et al. (2006b,a, 2009), provide a robust basis, they do not explicitly account for exogenous, forward-looking innovations. Building on this literature, we incorporate vitagions, defined as stochastic agents of mortality improvement associated with biomedical innovation and other external shocks (Woo (2014); Carannante et al. (2024)). Vitagions capture health-related advances, from disease prevention to advanced therapies, that can trigger persistent and one-sided mortality reductions.
This paper makes one main contribution. We extend the Lee–Carter (LC) and Cairns-Blake-Dowd M6 (CBD M6) models by adding an exogenous innovation covariate that captures age-specific sensitivity to a detrended indicator of pharmaceutical innovation (constructed from FDA/EMA approvals), and we address identifiability through explicit normalisations and orthogonality constraints. An empirical analysis employs data from the U.S., France, and Italy, which show different historical mortality patterns. Scenario-based simulations deliver clearer period dynamics while preserving baseline age profiles.
Keywords: stochastic mortality models; vitagions; longevity risk; Lee–Carter; Cairns–Blake–Dowd; medical innovation.