Longevity Risk: Actuarial and Predictive Models, Retirement Product Innovation, and Risk Management Strategies

  • About
  • Objectives and Aims
  • Papers
  • Conference Presentation
  • Research Team

Summary of Project Objectives

The project is a multi-year project spread over three years with four main objectives that address significant research issues for the actuarial profession in the area of longevity risk. They are interconnected and draw on the research backgrounds of the investigators. The project objectives are to:

  • Develop an actuarial and financial based framework for mortality and longevity risk modelling, drawing on the latest research in mathematical finance and longevity risk models;
  • Apply predictive modelling techniques to compare and assess mortality models;
  • Propose and analyse innovative structured retirement products incorporating investment, longevity and aged care/health risks; and
  • Propose and analyse the innovative design and assessment of risk management strategies aimed at mitigating financial and mortality risk.

Contribution to the Actuarial Profession

The actuarial profession has had a long tradition in life insurance and pensions as early pioneers in mortality models and application to insurance products. This project will further raise the profile of the profession in longevity risk research which is increasingly attracting attention from a range of disciplines. The project brings a multi-disciplinary approach to the issues by integrating financial and actuarial models. It will demonstrate the application of predictive analytics to mortality models, and extend knowledge of the models and applications of direct relevance and application for members of the profession. 
For SOA members we will present the research results at the major SOA conferences and publish research articles in the North American Actuarial Journal and other international peer reviewed actuarial journals. The researchers will be willing to run Webinars to present the results to SOA members on a regular basis and contribute to SOA events on longevity risk by travelling regularly to the US throughout the project. Anticipated distribution/publication of results includes presentation at the leading international actuarial, risk and insurance conferences and submission to the leading actuarial research journals. 

The project will increase the research links between UNSW and the SOA, including the Australian Research Council Centre of Excellence in Population Ageing Research (CEPAR) at UNSW. It will increase the links between the researchers and research students at UNSW with the SOA and increase the potential to attract high quality actuarial students to the UNSW actuarial program, many of whom will enter the profession and industry. The outcomes of the research aim on predictive analytics will enhance the teaching of data analytics in the actuarial curriculum more generally.

Objectives and Aims

1. A significant project aim is to develop an actuarial and financial based framework for mortality and longevity risk modelling drawing on the latest research in mathematical finance and longevity risk models.

This framework integrates financial risk models with actuarial models. The mortality models will extend and develop continuous state and time affine mortality rate models developed in actuarial science to include multiple populations-cohorts, capture dependence across ages and cohorts and allow more reliable estimation of expected future improvement trends for projection as well as risk-adjusted trends for pricing. Mortality uncertainty will be better captured through multiple risk factors, dependence structures across age and cohort that better reflect historical data and consistent construction of survival curves based on multiple factor dynamics. The framework will be applied to develop consistent multi-population models that allow quantification of basis risk between different groups of lives. The framework will include models for interest rates and equity returns, including Levy models, developed and extended from current research.

In addition, the research will also focus on mortality at the older ages, including the impact of mortality heterogeneity and health status. A range of models for heterogeneity including multiple health states and frailty models will be incorporated into the modelling framework. For long term care, models with functional disability will be incorporated and related to models of health status.

The continuous state and time affine mortality models are parsimonious, allow analytical solutions to survival probabilities, build on traditional financial and actuarial models, readily incorporate price of longevity risk, are readily estimated using Kalman filter, can be discretised for estimation and risk modelling and forecasting, and allow ready computation of risk distributions and solvency considerations. These features provide an innovative and powerful framework for the proposed project focusing on the innovative design, risk management and costing of retirement products.

2. An important second aim is to apply methods from predictive data analytics to compare and assess a range of mortality models including the continuous state and time models developed and proposed in the first project aim.

Discrete state and discrete time models dominate current mortality modelling, particularly the Lee-Carter model. This model has a large number of parameters to capture age trends, a single factor to capture uncertainty and is sensitive to the time period used for estimation. Other models such as the Cairns-Blake-Dowd model (CBD) are continuous state and incorporate multiple risk factors but do not provide a consistent framework and are not best suited for applications in a financial risk framework, usually requiring extensive simulations within simulations for actuarial applications. The aim will be to assess and compare the commonly used models along with the continuous state and continuous time models focusing on parameter and model risk using predictive analytic methods. These methods will include cross validation, training and performance evaluation, data splitting and resampling, penalized methods – LASSO, and robustness using ensemble methods, trees and outliers. The health status models will be assessed using longitudinal and panel data methods. Predictive analytic techniques are expected to demonstrate the advantages of using the parsimonious continuous time affine models for aggregate mortality models and allow a more reliable assessment of factors to include in the multiple health and functional state models.

3. A third aim is to use the model framework, particularly the continuous state and time affine mortality models and models of heterogeneity, to propose and analyse innovative structured retirement products incorporating investment, longevity and aged care/health risks.

The design of innovative risk sharing retirement products, is much needed as insurers and pension funds face the challenges of systematic mortality risk. Products such as group self annuitization products, deferred annuitization products, floating rate variable annuities and life care annuities incorporating payments dependent on functional disability are innovations that have been proposed. The extent to which these products meet the needs of an ageing population taking into account long run trends and uncertainty in mortality and health status remains relatively unexplored. This analysis will include portfolio strategies including self-insurance and phased withdrawals. Interest rate and equity risk will be included along with longevity risk. The incorporation of capital costs into the pricing of longevity product guarantees has received limited consideration in the literature. Solvency and capital implications for insurers and pension funds of these product innovations will be considered along with the risk management techniques of reinsurance and longevity derivatives in the final aim.

4. A final aim is to propose and analyse the innovative design and assessment of risk management strategies for use by insurers and pension funds aimed at mitigating financial and mortality risk.

To accomplish this the project aims to develop a value-based longevity index so that longevity-linked financial instruments can be assessed in terms of pricing and hedging. The index will incorporate historical, current and forecast levels of mortality trends by cohort based on the model development in the first aim of the project. This will use models and approaches that integrate financial and actuarial risks. Current indices are mostly based on survival probabilities and not the value of insurance obligations, making it difficult to measure and hedge the enterprise level provider risk using such indices. These indices are required for the development of financial and insurance contracts to transfer longevity and other risks to those who can most efficiently bear the risk. In addition, the analysis in the project will assist with developing liquidity and efficiency of markets, much needed to support innovation in the design of retirement income products and the required risk management strategies for product providers. Using a value based index, that includes financial and longevity risks, will provide a more effective benchmark to measure the effectiveness of hedging strategies such as reinsurance, natural hedging, longevity swaps, and innovations such as mortality linked options.

The project extends past research of the investigators on mortality and financial models, longevity and functional disability, longevity product pricing including complex guarantees, and insurer solvency and risk management as well as potential innovations in the risk transfer of longevity risk.


Papers

2017

Investigators at UNSW

Principal Investigator

Professor Michael Sherris
FSA, FIA, FIAA
Professor of Actuarial Studies and Chief Investigator CEPAR, UNSW

Prof Sherris is a Chief Investigator in the ARC Centre of Excellence in Population Ageing Research and the Foundation Professor of the Actuarial program at UNSW. He has successfully been lead investigator on a number of large multi-year ARC research grants and is a Chief Investigator in the ARC Centre of Excellence in Population Ageing Research (CEPAR). These grants have supported 11 PhD students, 11 honours (1-year research) students and 10 postdoctoral researchers at UNSW. They have involved industry partners and have resulted in a number of prize winning papers published in leading international actuarial journals.

Investigators

Dr Jonathan Ziveyi
Senior Lecturer in the School of Risk and Actuarial Studies and Associate Investigator CEPAR, UNSW

Dr Ziveyi contributes a background in financial mathematics and actuarial models to the project which includes numerical techniques for implementation of financial models and the assessment of guarantees depending on mortality and financial risks. He has collaborated with Prof Sherris on a number of projects in the area of longevity risk. 

Dr Andrés Villegas 
Lecturer in the School of Risk and Actuarial Studies from 2017 and Associate Investigator CEPAR, UNSW 

Dr Villegas brings an actuarial background with extensive research in longevity risk, mortality heterogeneity and a strong practical and applied focus. In 2017 he joined the Faculty of the School of Risk and Actuarial Studies as lecturer after a period as a postdoctoral researcher in the ARC Centre of Excellence in Population Ageing Research. He is collaborating with Dr Ziveyi and Prof Sherris including joint supervision of PhD students.

Associate Investigators

Dr Adam Wenqiang Shao
ASA
Milliman, Associate Investigator CEPAR, UNSW

Dr Shao is a former PhD student in the School and brings a background in multi-state health transition models. He is an Associate Investigator in the ARC Centre of Excellence in Population Ageing Research and an Actuarial Consultant at Milliman focusing on financial risk management.

Prof Annamaria Olivieri
University of Parma and Associate Investigator CEPAR, UNSW

Prof Olivieri is Associate Investigator in CEPAR at UNSW and is internationally recognised leaders in mortality and health status modelling, longevity risk and insurance. 

Prof Ermanno Pitacco
University of Trieste, Associate Investigator CEPAR, UNSW and Member of IAA Mortality Working Group
Prof Pitacco is Associate Investigator in CEPAR at UNSW and is internationally recognised leaders in mortality and health status modelling, longevity risk and insurance. 

Research Students and Assistants

Xiao Xu
FSA
PhD Candidate

Yulong Li
PhD Candidate
Completed 5 preliminary SOA exams and Chinese Society of Actuaries exams

Shianna Li 
MPhil Candidate

Yajing Xu
Former PhD Candidate
Completed ASA examinations

Mengyi Xu
Former PhD Candidate
Completing Actuaries Institute Fellowship examinations