Actuarial and Financial Mathematics

What we do

We are one of the largest Actuarial and Financial Mathematics research groups in the UK with a broad range of both applied and theoretical research interests. The group has a strong record of engagement with industry and other users of its research leading to several important impact case studies, reflecting its location in Edinburgh, one of Europe's leading centres for financial services.

The Group organises regular seminars in Actuarial and Financial Mathematics, to complement those in Probability and Statistics and we have strong links to the Maxwell Institute.

Specific areas of the group’s activity include:

Mortality, Longevity and Morbidity Analysis

  • Modelling and management of mortality and longevity risk
  • Genetics and insurance
  • Morbidity modelling
  • Bayesian modelling in morbidity and mortality studies
  • Analysis of mortality by cause of death
  • Analysis of socio-economic inequalities in mortality and morbidity data
  • Financial risk management of longevity risk
  • Understanding the impact of the Covid-19 pandemic

Applications of Data Science to Actuarial and Financial Research Problems

  • Statistical learning in non-life insurance and finance
  • Predictive modelling and uncertainty quantification for morbidity risk
  • Decision making in insurance using machine learning and data analytics
  • Reinforcement and online learning applications

Actuarial Mathematics

  • Application of Bayesian computational methods to problems arising in insurance
  • Life and health insurance and products
  • Risk sharing and optimal (re)insurance
  • Optimal control problems
  • Model and parameter risk in insurance and pensions

Pensions and Social Security

  • Optimal design of pension products
  • Solvency of pension plans
  • Actuarial fairness
  • Pension reforms
  • Mixed schemes
  • Automatic balancing mechanisms
  • Risk-sharing

Quantitative Risk Management

  • Risk management for life insurers and pension plans
  • Risk measures
  • Economic capital allocation problems
  • Risk aggregation and resource optimisation
  • Risk optimisation
  • Emerging risk management: cyber, pandemic, and climate
  • Credit risk management

Finance and Economics

  • Ethics in finance
  • Classification of green bonds using statistical learning methods
  • Behavioural methods in economics and finance
  • Decarbonization and sustainability

Financial Mathematics

  • Application of stochastic analysis to mathematical finance
  • Computational finance
  • Monte Carlo methods for tackling problems in financial mathematics
  • Optimal control problems in the energy markets
  • Stochastic asset models
  • Interest rate models
  • Liquidity risk and liquidity premiums
  • Forward preferences and control strategies
  • Time-inconsistent control and its applications on behavioural economics and finance

Software and Data Resources

Bonds Database

David Wilkie and Andrew Cairns have built up a substantial database for UK government bonds with financial support from the Institute and Faculty of Actuaries. This includes prices, amounts in issue, index values and details of each security in issue. The database is updated on a regular basis.


Andrew Cairns is co-inventor of the CBD stochastic mortality models and author of the LifeMetrics open source R code for fitting stochastic mortality models that can be used for modelling, measurement and management of longevity risk.

LIFE app

Andrew Cairns, Jie Wen and Torsten Kleinow have developed the Longevity Index for England (LIFE) that measures mortality inequalities across England. To help stakeholders gain a better understanding of mortality inequalities they have developed the LIFE App.


Tim Johnson is author of Ethics in Quantitative Finance published by Springer in 2017.

Group Members

Ayse ArikCarmen Boado PenasAndrew Cairns, Alfred Chong Catherine DonnellyAbdul-Lateef Haji-Ali Tim Johnson, Angus Macdonald, Giovanni Rabitti, George Streftaris, George Tzougas, Wei WeiAnke WieseJing Yao 

Modelling, Measurement & Management of Longevity Risk by Professor Andrew Cairns