Nonparametric Estimation of Some Dividend and Ruin Related Functions in a Lévy Risk Model

In this paper, we consider the statistical estimation of some dividend-related functions in a spectrally negative Lévy risk model under the constant barrier dividend strategy. We assume that the insurance company's surplus flow without dividend payments is modeled by a general spectrally negative Lévy process, and we obtain a dataset of aggregate claims and aggregate dividends based on low-frequency sampling observation. The dividend-related functions are estimated by the Fourier cosine method and the convergence rates of the estimators are derived. Extensive numerical experiments demonstrate that our estimators are very effective when the sample size is finite.