Semiparametric Estimation for Non-Ruin Probabilities

Konstadinos Politis

Scandinavian Actuarial Journal, 2003, vol. 2003, issue 1, 75-96

Abstract: We consider the classical risk model with unknown claim size distribution F and unknown Poisson arrival rate u . Given a sample of claims from F and a sample of interarrival times for these claims, we construct an estimator for the function Z ( u ), which gives the probability of non-ruin in that model for initial surplus u . We obtain strong consistency and asymptotic normality for that estimator for a large class of claim distributions F . Confidence bounds for Z ( u ) based on the bootstrap are also given and illustrated by some numerical examples.

Date: 2003
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DOI: 10.1080/03461230308487

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