Peter Hieber, Nathalie Lucas

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The tendency of insurance providers to refrain from offering long-term guarantees on investment or mortality risk has shifted attention to mutual risk pooling schemes like (modern) tontines, pooled annuities or group self annuitization schemes. While the literature has focused on mortality risk pooling schemes, this paper builds on the advantage of pooling mortality and morbidity risks, and their inherent natural hedge. We introduce a modern life-care tontine, which in addition to retirement income targets the needs of long-term care (LTC) coverage for an ageing population. In contrast to a classical life-care annuity, both mortality and LTC risks are shared within the policyholder pool by mortality and morbidity credits, respectively. Technically, we rely on a backward iteration to deduce the smoothed cashflows pattern and the separation of cash-flows in a fixed withdrawal and a surplus from the two types of risks. We illustrate our results using real life data, demonstrating the adequacy of the proposed tontine scheme.

Original languageEnglish
Pages (from-to)563-589
Number of pages27
JournalASTIN Bulletin
Issue number2
StatePublished - 5 May 2022
Externally publishedYes


  • Mutual insurance
  • life-care insurance
  • long-term care
  • morbidity and mortality risk
  • pooled annuities
  • tontines


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