Aggregation of 1-year risks in life and disability insurance

Boualem Djehiche, Bjorn Lofdahl

Research output: Contribution to journalArticlepeer-review


We consider large insurance portfolios consisting of life or disability insurance policies that are assumed independent, conditional on a stochastic process representing the economic-demographic environment. Using the conditional law of large numbers, we show that when the portfolio of liabilities becomes large enough, its value on a δ-year horizon can be approximated by a functional of the environment process. Based on this representation, we derive a semi-analytical approximation of the systematic risk quantiles of the future liability value for a homogeneous portfolio when the environment is represented by a one-factor diffusion process. For the multi-factor diffusion case, we propose two different risk aggregation techniques for a portfolio consisting of large, homogeneous pools. We give numerical results comparing the resulting capital charges with the Solvency II standard formula, based on disability claims data from the Swedish insurance company Folksam.

Original languageEnglish (US)
Pages (from-to)203-221
Number of pages19
JournalAnnals of Actuarial Science
Issue number2
StatePublished - Aug 22 2016


  • Conditional law of large numbers
  • Disability insurance
  • Life insurance
  • Risk aggregation
  • Solvency capital requirements

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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