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Nonparametric estimation of the finite time ruin probability in the classical risk model

In this paper, we consider the nonparametric estimation of the finite time ruin probability in the classical risk model. Suppose that the individual claim size distribution is unknown, but a random sample of claims is available. We construct the estimator by double Fourier transform. The asymptotic properties of the estimator are studied under large sample setting, and show that an almost convergence rate can be obtained. Some simulation examples are also provided to illustrate the performance of the estimator under finite sample size setting.