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On ruin probabilities in risk models with interest rate

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Nino Kordzakhia

    (Macquarie University)

  • Alexander Novikov

    (University of Technology)

  • Gurami Tsitsiashvili

    (Institute of Applied Mathematics)

Abstract

An explicit formula for the finite-time ruin probability in a discrete-time collective ruin model with constant interest rate is found under the assumption that claims follow a generalised hyperexponential distribution. The formula can be used for finding approximations for finite-time ruin probabilities in the case when claim sizes follow a heavy-tailed distribution e.g. Pareto. We also provide theoretical bounds for the accuracy of approximations of the finite-time ruin probabilities in terms of a distance between the distribution of claims and its approximation. Results of numerical comparisons with asymptotic formulas and simulations are presented.

Suggested Citation

  • Nino Kordzakhia & Alexander Novikov & Gurami Tsitsiashvili, 2012. "On ruin probabilities in risk models with interest rate," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 245-253, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2342-0_29
    DOI: 10.1007/978-88-470-2342-0_29
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