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1 results

  • Moderate- and large-deviation probabilities in actuarial risk theory

  • Eric Slud, Craig Hoesman
  • Journal:
    Advances in Applied Probability / Volume 21 / Issue 4 / December 1989
    Published online by Cambridge University Press:
    01 July 2016, pp. 725-741
    Print publication:
    December 1989

  • A general model for the actuarial risk-reserve process as a superposition of compound delayed-renewal processes is introduced and related to previous models which have been used in collective risk theory. It is observed that non-stationarity of the portfolio ‘age-structure' within this model can have a significant impact upon probabilities of ruin. When the portfolio size is constant and the policy age-distribution is stationary, the moderate- and large-deviation probabilities of ruin are bounded and calculated using the strong approximation results of Csörg et al. (1987a, b) and a large-deviation theorem of Groeneboom et al. (1979). One consequence is that for non-Poisson claim-arrivals, the large-deviation probabilities of ruin are noticeably affected by the decision to model many parallel policy lines in place of one line with correspondingly faster claim-arrivals.