Total duration of negative surplus for the dual model

Min Song*, Rong Wu, Xin Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In the dual model, we allow the surplus process to continue if the surplus falls below zero. By introducing the renewal measure of the defective renewal sequence constituted by the zero points of the surplus process, we obtain the probability of hitting the zero point. Further, we derive formulae for the Laplace transform, expectation and variance of total duration of negative surplus and present some examples with an exponential individual jump amount distribution.

Original languageEnglish
Pages (from-to)591-600
Number of pages10
JournalApplied Stochastic Models in Business and Industry
Issue number6
Publication statusPublished - Nov 2008


  • Compound poisson risk process
  • Dual model
  • Hitting probability
  • Ruin probability
  • Total duration of negative surplus

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