Confidence intervals of ruin probability under Lévy surplus

2021/12/14 by Yasutaka Shimizu, Shimizu, Yasutaka
Decision Sciences · Mathematics · Social Sciences · #Insurance, Mortality, Demography, Risk Management #Probability and Risk Models #Statistical Distribution Estimation and Applications #math.PR #stat.AP #stat.ME

paper · pdf · doi:10.48550/arxiv.2112.07405

arxiv created 2021/12/14 · arxiv updated 2021/12/15

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 Cramér-type approximation for the derivative and gives an asymptotic confidence interval of ruin probability.

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