Confidence intervals of ruin probability under Lévy surplus
Abstract
The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a Lévy process. Assuming a parametric family for the Lévy measures, we estimate the parameter from the surplus data and estimate the ruin probability via the delta method. However the asymptotic variance includes the derivative of the ruin probability with respect to the parameter, which is not generally given explicitly, and the confidence interval is not straightforward even if the ruin probability is well estimated. This paper gives the Cramértype approximation for the derivative and gives an asymptotic confidence interval of ruin probability.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2112.07405
 Bibcode:
 2021arXiv211207405S
 Keywords:

 Mathematics  Probability;
 Statistics  Applications;
 Statistics  Methodology