General tax structures for a Lévy insurance risk process under the Cramér condition

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We investigate the Lévy insurance risk model with tax under Cramér's condition. A direct analogue of Cramér's estimate for the probability of ruin in this model is obtained, together with the asymptotic distribution, conditional on ruin occurring, of several variables of interest related to ruin including the surplus immediately prior to ruin (undershoot) and shortfall at ruin (overshoot). We also compute the present value of all tax paid conditional on ruin occurring. The proof involves first transferring results from the model with no tax to the reflected process, and from there to the model with tax.

Original languageEnglish (US)
Pages (from-to)1368-1387
Number of pages20
JournalStochastic Processes and their Applications
Issue number3
StatePublished - Mar 2020


  • Cramér condition
  • First passage time
  • Lévy insurance risk process
  • Overshoot
  • Reflected process
  • Tax structures

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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