Nonlinear reserving in life insurance: Aggregation and mean-field approximation

Boualem Djehiche, Björn Löfdahl

Research output: Contribution to journalArticlepeer-review


We suggest a unified approach to claims reserving for life insurance policies with reserve-dependent payments driven by multi-state Markov chains. The associated prospective reserve is formulated as a recursive utility function using the framework of backward stochastic differential equations (BSDE). We show that the prospective reserve satisfies a nonlinear Thiele equation for Markovian BSDEs when the driver is a deterministic function of the reserve and the underlying Markov chain. Aggregation of prospective reserves for large and homogeneous insurance portfolios is considered through mean-field approximations. We show that the corresponding prospective reserve satisfies a BSDE of mean-field type and derive the associated nonlinear Thiele equation.

Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalInsurance: Mathematics and Economics
StatePublished - Jul 1 2016


  • Backward stochastic differential equation
  • Life insurance
  • Markov process
  • Mean-field
  • Multistate models
  • Surrender value
  • Thiele's equation

ASJC Scopus subject areas

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


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