Nonparametric estimation for a spectrally negative Lévy risk process based on low-frequency observation

摘要

In this paper, we study nonparametric estimation of survival probability for a spectrally negative Lévy risk model based on low-frequency observation. The estimator of survival probability is constructed via a regularized version of the inverse of the Laplace transform. The convergence rate of the estimator in a sense of the integrated squared error (ISE) is studied for large sample size. We propose a method of simulation to show the finite sample performance of our estimator.