Probability Distributions of Multi-States Insurance Models under Semi-Markov Assumptions

Franck Adékambi, Marcus Christiansen

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this paper we develop integral and differential backward equation systems for the state-wise cumulative distribution functions of the discounted future cash-flow of multi-states life and health insurance policies, assuming that the state process of the insured is semi-Markovian. We derive equation systems in two different ways: First, we apply the inversion method on the state-wise moment generating function. Second, we apply a transformation trick on the state-wise cumulative distribution functions. The results are illustrated with applications to Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR) calculations.

Original languageEnglish
Pages (from-to)517-534
Number of pages18
JournalMarkov Processes and Related Fields
Issue number3
Publication statusPublished - 2020


  • Value-at-Risk
  • backward equations
  • life and health insurance
  • semi-Markov model
  • state-wise probability dis-tributions

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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