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1 results

  • Nonparametric Estimation of the Probability of Ruin

  • Edward W. Frees
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 16 / Issue S1 / April 1986
    Published online by Cambridge University Press:
    29 August 2014, pp. S81-S90
    Print publication:
    April 1986
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  • The finite and infinite horizon time probability of ruin are important parameters in the study of actuarial risk theory. This paper introduces procedures for directly estimating these key parameters from a random sample of observations without assumptions as to the parametric form of the distribution from which the observations arise. The estimators introduced apply to most of the classical models in which ruin probabilities are used and also apply to a much broader class of models. The procedures are based on the concept of sample reuse, an old idea in statistics which is becoming more popular due to the widespread availability of high speed computers. In this paper, the almost sure consistency of the estimators is established. Further, finite sample properties of the estimators are investigated in a simulation study.