Lundberg inequalities for a Cox model with a piecewise constant intensity

Hanspeter Schmidli

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33 Citations (Scopus)


A Cox risk process with a piecewise constant intensity is considered where the sequence (Li) of successive levels of the intensity forms a Markov chain. The duration s, of the level Li is assumed to be only dependent via Li. In the small-claim case a Lundberg inequality is obtained via a martingale approach. It is shown furthermore by a Lundberg bound from below that the resulting adjustment coefficient gives the best possible exponential bound for the ruin probability. In the case where the stationary distribution of Li contains a discrete component, a Cramér-Lundberg approximation can be obtained. By way of example we consider the independent jump intensity model (Björk and Grandell 1988) and the risk model in a Markovian environment (Asmussen 1989).

Original languageEnglish
Pages (from-to)196-210
Number of pages15
JournalJournal of Applied Probability
Issue number1
Publication statusPublished - Mar 1996


  • Change of measure
  • Cox model
  • Cramér-Lundberg approximation
  • Lundberg inequality
  • Martingale methods
  • Risk theory
  • Ruin probability


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