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Lundberg-type Bounds and Asymptotics for the Moments of the Time to Ruin

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Abstract

We obtain analogues of Lundberg’s inequality and the Cramér—Lundberg asymptotic relationship for the k-th moment of the time to ruin in the classical risk model. We also derive the asymptotic behaviour of the mean time to ruin when the claim size distribution has a heavy or intermediate tail.

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Authors and Affiliations

  1. Department of Statistics and Insurance, University of Piraeus, 80 Karaoli and Demetriou Street, Piraeus, 18534, Greece

    Vaios Dermitzakis & Konstadinos Politis

  2. Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK

    Susan M. Pitts

Authors
  1. Vaios Dermitzakis
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  2. Susan M. Pitts
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  3. Konstadinos Politis
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Correspondence to Susan M. Pitts.

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Dermitzakis, V., Pitts, S.M. & Politis, K. Lundberg-type Bounds and Asymptotics for the Moments of the Time to Ruin. Methodol Comput Appl Probab 12, 155–175 (2010). https://doi.org/10.1007/s11009-008-9102-6

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  • DOI: https://doi.org/10.1007/s11009-008-9102-6

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