Risk aggregation and stochastic claims reserving in disability insurance

Boualem Djehiche, Björn Löfdahl

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic-demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving and risk aggregation for large portfolios. Further, we derive a partial differential equation for moments of present values. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for solving the PDEs very efficiently. Finally, we give a numerical example where moments of present values of disability annuities are computed using finite-difference methods and Monte Carlo simulations.

Original languageEnglish (US)
Pages (from-to)100-108
Number of pages9
JournalInsurance: Mathematics and Economics
Volume59
DOIs
StatePublished - 2014

Keywords

  • Conditional independence
  • Disability insurance
  • Mimicking
  • Risk aggregation
  • Stochastic claims reserving
  • Stochastic intensities

ASJC Scopus subject areas

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

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