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Nonparametric estimation for a spectrally negative Lévy risk process based on low-frequency observation. (English) Zbl 1391.62193

Summary: 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.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60G51 Processes with independent increments; Lévy processes
62G05 Nonparametric estimation
62N05 Reliability and life testing
91B30 Risk theory, insurance (MSC2010)
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