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Nonparametric estimation for a spectrally negative Lévy process based on high frequency data. (English) Zbl 1402.62262

Summary: In this paper, we consider the nonparametric estimation of the survival probability for a spectrally negative Lévy risk model based on high frequency data. We use a regularized Laplace inversion technique to obtain the estimator of survival probability. A rate of convergence in probability for the integrated squared error (ISE) is derived. Simulation studies are also given to show the finite sample performance of our estimator.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62G05 Nonparametric estimation
60G51 Processes with independent increments; Lévy processes
91B30 Risk theory, insurance (MSC2010)
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