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Risks
Special Issues
Longevity Risk Modelling and Management
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Longevity Risk Modelling and Management

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 16242

Special Issue Editors

Prof. Michael Sherris

E-Mail Website
Guest Editor
Risk and Actuarial Studies and Centre of Excellence in Population Ageing Research (CEPAR), UNSW Business School, University of New South Wales, Sydney, NSW 2052, Australia
Interests: longevity risk; mortality models; long-term care insurance; retirement financing; quantitative risk management
Dr. Katja Hanewald

E-Mail Website
Guest Editor
Risk and Actuarial Studies and Centre of Excellence in Population Ageing Research (CEPAR), UNSW Business School, University of New South Wales, Sydney, NSW 2052, Australia
Interests: insurance; risk management; actuarial studies; longevity risk management; retirement financial products; ageing in china

Special Issue Information

Dear Colleagues,

The modelling and management of longevity risk has seen many advances over recent years. Increasing attention is being paid to richer models incorporating explanatory risk factors and the application of data analytic techniques to mortality data. Health status models and their application to long-term care insurance has broadened the potential products available for the individual management of longevity risk. Innovations in product designs, including combinations of annuities and long-term care insurance, reverse mortgages, and long-term care insurance, as well as with pooled annuities, such as group self-annuitization and modified forms of tontines, are broadening the product menu for individuals in order to manage their longevity risk. Life insurers and pension funds also have important roles to play in financing individual longevity and health risks, based on a more comprehensive understanding of these risks.

Against this background, there are many areas of longevity risk modelling and management that can benefit from novel research in both methodology and application. These include continuous time mortality models; panel data models for individual mortality risk factors; the integration of health status and aggregate mortality models; data analytic techniques applied to longevity risk modelling; multiple population models; spatial modelling of longevity risk; the design of innovative contracts, such as pooled annuities, age-care annuities, enhanced annuities, variable annuities with guaranteed withdrawal benefits, and reverse mortgages combined with long-term care insurance; retirement financing strategies for individuals allowing for health risk, housing, and equity investment; demand modelling for longevity risk products; life insurer longevity risk management, including longevity swaps and securitization; insurer capital requirements for longevity risk; pensions fund longevity risk management; and investment strategies for longevity risk such as liability driven investment strategies.

The aim of this Special Issue is to present leading-edge research articles focussed on the current aspects of longevity risk modelling and management. Comprehensive survey papers, as the basis for future research ideas, will also be considered.

Prof. Michael Sherris
Dr. Katja Hanewald
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Risks is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Mortality models
  • Longevity risk
  • Retirement product innovation
  • Health status models
  • Data analytic techniques applied to longevity
  • Reverse mortgages
  • Variable annuities
  • Pooled annuities
  • Optimal individual retirement decision making
  • Life insurer and pension fund longevity risk management
  • Securitization of longevity risk

Published Papers (7 papers)

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Research

28 pages, 890 KiB  
Article
Modelling USA Age-Cohort Mortality: A Comparison of Multi-Factor Affine Mortality Models
by Zhiping Huang, Michael Sherris, Andrés M. Villegas and Jonathan Ziveyi
Risks 2022, 10(9), 183; https://doi.org/10.3390/risks10090183 - 15 Sep 2022
Cited by 2 | Viewed by 1922
Abstract
Affine mortality models are well suited for theoretical and practical application in pricing and risk management of mortality risk. They produce consistent, closed-form stochastic survival curves allowing for the efficient valuation of mortality-linked claims. We model USA age-cohort mortality data using five multi-factor [...] Read more.
Affine mortality models are well suited for theoretical and practical application in pricing and risk management of mortality risk. They produce consistent, closed-form stochastic survival curves allowing for the efficient valuation of mortality-linked claims. We model USA age-cohort mortality data using five multi-factor affine mortality models. We focus on three-factor models and compare four Gaussian models along with a model based on the Cox–Ingersoll–Ross (CIR) process, allowing for Gamma-distributed mortality rates. We compare and assess the Gaussian Arbitrage-Free Nelson–Siegel (AFNS) mortality model, which incorporates level, slope and curvature factors, and the canonical Gaussian factor model, both with and without correlations in the factor dynamics. We show that for USA mortality data, the probability of negative mortality rates in the Gaussian models is small. Models are estimated using discrete time versions of the models with age-cohort data capturing variability in cohort mortality curves. Poisson variation in mortality data is included in the model estimation using the Kalman filter through the measurement equation. We consider models incorporating factor dependence to capture the effects of age-dependence in the mortality curves. The analysis demonstrates that the Gaussian independent-factor AFNS model performs well compared to the other affine models in explaining and forecasting USA age-cohort mortality data. Full article
(This article belongs to the Special Issue Longevity Risk Modelling and Management)
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18 pages, 460 KiB  
Article
Time Restrictions on Life Annuity Benefits: Portfolio Risk Profiles
by Annamaria Olivieri and Ermanno Pitacco
Risks 2022, 10(8), 164; https://doi.org/10.3390/risks10080164 - 12 Aug 2022
Viewed by 1452
Abstract
Due to the increasing interest in several markets in life annuity products with a guaranteed periodic benefit, the back-side effects of some features that may prove to be critical either for the provider or the customer should be better understood. In this research, [...] Read more.
Due to the increasing interest in several markets in life annuity products with a guaranteed periodic benefit, the back-side effects of some features that may prove to be critical either for the provider or the customer should be better understood. In this research, we focus on the time frames defined by the policy conditions of life annuities. While the payment phase coincides with the post-retirement period in the traditional annuity product, arrangements with alternative time frames are being offered in the market. Time restrictions, in particular, could be welcomed both by customers and providers, as they result in a reduction in expected costs and equivalence premiums. However, due to the different impact of longevity risk on different age ranges, time restrictions could increase risks to the provider, at least in relative terms. On the other hand, time restrictions reduce the duration of the provider’s liability, which should therefore be less exposed to financial risk. We focus on this issue, examining the probability distribution of the total portfolio payout resulting from alternative time frames for life annuity arrangements, first addressing longevity risk only, and then including also financial risk. The discussion is developed in view of understanding whether a reduction in the equivalence premium implied by time restrictions should be matched by higher premium loading and required capital rates. Full article
(This article belongs to the Special Issue Longevity Risk Modelling and Management)
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30 pages, 587 KiB  
Article
A Managed Volatility Investment Strategy for Pooled Annuity Products
by Shuanglan Li, Héloïse Labit Hardy, Michael Sherris and Andrés M. Villegas
Risks 2022, 10(6), 121; https://doi.org/10.3390/risks10060121 - 10 Jun 2022
Cited by 2 | Viewed by 2153
Abstract
Pooled annuity products, where the participants share systematic and idiosyncratic mortality risks as well as investment returns and risk, provide an attractive and effective alternative to traditional guaranteed life annuity products. While longevity risk sharing in pooled annuities has received recent attention, incorporating [...] Read more.
Pooled annuity products, where the participants share systematic and idiosyncratic mortality risks as well as investment returns and risk, provide an attractive and effective alternative to traditional guaranteed life annuity products. While longevity risk sharing in pooled annuities has received recent attention, incorporating investment risk beyond fixed interest returns is relatively unexplored. Incorporating equity investments has the potential to increase expected annuity payments at the expense of higher variability. We propose and assess a strategy for incorporating equity investments along with managed-volatility for pooled annuity funds. We show how the managed volatility strategy improves investment performance, while reducing pooled annuity income volatility and downside risk, as well as an investment strategy that reduces exposure to investment risk over time. We quantify the impact of pool size when equity investments are included, showing how these products are viable with relatively small pool sizes. Full article
(This article belongs to the Special Issue Longevity Risk Modelling and Management)
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17 pages, 839 KiB  
Article
Analyzing How the Social Security Reserve Fund in Spain Affects the Sustainability of the Pension System
by Emilio Gómez-Déniz, Jorge V. Pérez-Rodríguez and Simón Sosvilla-Rivero
Risks 2022, 10(6), 120; https://doi.org/10.3390/risks10060120 - 10 Jun 2022
Viewed by 1683
Abstract
Faced with the need to adjust public pension systems to meet changing demographic, economic and social conditions, most developed countries have created government reserve funds to ensure macroeconomic sustainability. This paper aims to study the importance that this reserve fund plays in the [...] Read more.
Faced with the need to adjust public pension systems to meet changing demographic, economic and social conditions, most developed countries have created government reserve funds to ensure macroeconomic sustainability. This paper aims to study the importance that this reserve fund plays in the sustainability of the Spanish public pension system. Using data for the 2000 to 2019 period (20 observations) on the main variables impacting on the system, we calculate probabilities and other indicators of its unsustainability in relation to the reserve fund. Our model accurately reflects certain aspects of the data, and suggests that the probability of unsustainability is inversely associated with the size of the reserve fund, but that this relation is moderated by the heterogeneity of the members of the pension system. Moreover, the probability of unsustainability increases in line with the pension system deficit, the time elapsed until unsustainability is reached is shorter when the Reserve Fund balance falls, and the size of this fund at which the system becomes unsustainable diminishes with the probability of unsustainability. Full article
(This article belongs to the Special Issue Longevity Risk Modelling and Management)
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30 pages, 3163 KiB  
Article
Common Factor Cause-Specific Mortality Model
by Geert Zittersteyn and Jennifer Alonso-García
Risks 2021, 9(12), 221; https://doi.org/10.3390/risks9120221 - 03 Dec 2021
Cited by 1 | Viewed by 2289
Abstract
Recent pension reforms in Europe have implemented a link between retirement age and life expectancy. The accurate forecast of life tables and life expectancy is hence paramount for governmental policy and financial institutions. We developed a multi-population mortality model which includes a cause-specific [...] Read more.
Recent pension reforms in Europe have implemented a link between retirement age and life expectancy. The accurate forecast of life tables and life expectancy is hence paramount for governmental policy and financial institutions. We developed a multi-population mortality model which includes a cause-specific environment using Archimedean copulae to model dependence between various groups of causes of death. For this, Dutch data on cause-of-death mortality and cause-specific mortality data from 14 comparable European countries were used. We find that the inclusion of a common factor to a cause-specific mortality context increases the robustness of the forecast and we underline that cause-specific mortality forecasts foresee a more pessimistic mortality future than general mortality models. Overall, we find that this non-trivial extension is robust to the copula specification for commonly chosen dependence parameters. Full article
(This article belongs to the Special Issue Longevity Risk Modelling and Management)
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21 pages, 2337 KiB  
Article
Subnational Mortality Modelling: A Bayesian Hierarchical Model with Common Factors
by Qian Lu, Katja Hanewald and Xiaojun Wang
Risks 2021, 9(11), 203; https://doi.org/10.3390/risks9110203 - 10 Nov 2021
Cited by 1 | Viewed by 2104
Abstract
We propose a new model in a Bayesian hierarchical framework to project mortality at both national and subnational levels based on sparse or missing data. The new model, which has a country–region–province structure, uses common factors to pool information at the national level [...] Read more.
We propose a new model in a Bayesian hierarchical framework to project mortality at both national and subnational levels based on sparse or missing data. The new model, which has a country–region–province structure, uses common factors to pool information at the national level and within regions consisting of several provinces or states. We illustrate the model’s use by drawing on a new database containing provincial-level mortality data for China from four censuses conducted during the period 1982–2010. The new model provides good estimates and reasonable forecasts at both the country and provincial levels. The model’s forecast intervals reflect provincial- and regional-level uncertainty. Using subnational data for the period 1999–2018 from the Centers for Disease Control and Prevention (CDC), we also apply the model to the United States. We use mortality forecasts to compute and compare national and subnational life expectancies for China and the United States. The model predicts that, in 2030, China will have a similar national life expectancy at age 60 and a similar heterogeneity in subnational life expectancy as the United States. Full article
(This article belongs to the Special Issue Longevity Risk Modelling and Management)
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21 pages, 582 KiB  
Article
Coherent Mortality Forecasting for Less Developed Countries
by Hong Li, Yang Lu and Pintao Lyu
Risks 2021, 9(9), 151; https://doi.org/10.3390/risks9090151 - 24 Aug 2021
Cited by 4 | Viewed by 2219
Abstract
This paper proposes a coherent multi-population approach to mortality forecasting for less developed countries. The majority of these countries have witnessed faster mortality declines among the young and the working age populations during the past few decades, whereas in the more developed countries, [...] Read more.
This paper proposes a coherent multi-population approach to mortality forecasting for less developed countries. The majority of these countries have witnessed faster mortality declines among the young and the working age populations during the past few decades, whereas in the more developed countries, the contemporary mortality declines have been more substantial among the elders. Along with the socioeconomic developments, the mortality patterns of the less developed countries may become closer to those of the more developed countries. As a consequence, forecasting the long-term mortality of a less developed country by simply extrapolating its historical patterns might lead to implausible results. As an alternative, this paper proposes to incorporate the mortality patterns of a group of more developed countries as the benchmark to improve the forecast for a less developed one. With long-term, between-country coherence in mind, we allow the less developed country’s age-specific mortality improvement rates to gradually converge with those of the benchmark countries during the projection phase. Further, we employ a data-driven, threshold hitting approach to control the speed of this convergence. Our method is applied to China, Brazil, and Nigeria. We conclude that taking into account the gradual convergence of mortality patterns can lead to more reasonable long-term forecasts for less developed countries. Full article
(This article belongs to the Special Issue Longevity Risk Modelling and Management)
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