Related Risk Models

  • Gordon E. Willmot
  • Jae-Kyung Woo
Part of the Springer Actuarial book series (SPACT)


A similar surplus analysis as that of previous chapters, but with important variations on the dependent Sparre Andersen model, is considered in this chapter. In Sect. 7.1, the joint distribution of the first interclaim time and claim size distributions is allowed to assume a different form in order to accomodate the possibility that a claim does not occur at time 0. A special case of this model involving the equilibrium distribution of subsequent (marginal) interclaim times, motivated by stationarity arguments, is also discussed. A discrete model is considered in Sect. 7.2, where special emphasis is placed on analysis using a discrete Coxian type assumption for the (marginal) interclaim times. This model generalizes the compound binomial model, a discrete analog of the classical Poisson model often used in financial applications, which is discussed here as well.

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada
  2. 2.School of Risk and Actuarial StudiesUniversity of New South WalesSydneyAustralia

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