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Nonparametric Estimation of the Probability of Ruin

Published online by Cambridge University Press:  29 August 2014

Edward W. Frees
Edward W. Frees*
Affiliation:
University of Wisconsin-Madison
*
School of Business, University of Wisconsin-Madison, 1155 Observatory Drive, Madison, WI53706, USA
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Abstract

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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.

Keywords

Reverse martingalesample reuse
Type
Astin Competition 1985: Prize-Winning Papers and Other Selected Papers
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue S1 , April 1986 , pp. S81 - S90
Copyright
Copyright © International Actuarial Association 1986

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