Title: Asymptotically normal estimators of the ruin probability for Levy insurance risks
Authors: Yasutaka Shimizu - Waseda University (Japan) [presenting]
Abstract: A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a Levy insurance risk. The surplus model is a spectrally negative Levy process with diffusion terms and possibly infinite activity jumps. We assume that the observations are discrete equi-distant records of the surplus, and large jumps (claims). We consider the Laguerre series expansion of the ruin probability and give an estimator of the partial sum, which is an approximation of the ruin probability in L2-sense. Under a high-frequent observation scheme, we show the asymptotic normality of the proposed estimator with the estimable asymptotic variance. This estimator enables not only a point estimation of ruin probability, but also an interval estimation and a testing hypothesis.