Cai, Chunhao; Chen, Nan; You, Honglong Nonparametric estimation for a spectrally negative Lévy risk process based on low-frequency observation. (English) Zbl 1391.62193 J. Comput. Appl. Math. 328, 432-442 (2018). 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. Cited in 6 Documents 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) Keywords:survival probability; nonparametric estimation; Laplace transform; spectrally negative Lévy process; regularized Laplace inversion transform; risk model PDFBibTeX XMLCite \textit{C. Cai} et al., J. Comput. Appl. Math. 328, 432--442 (2018; Zbl 1391.62193) Full Text: DOI References: [1] Bening, V. E.; Korolev, V. Y., Nonparametric estimation of the ruin probability for generalized risk processes, Theory Probab. Appl., 47, 1, 1-16 (2002) · Zbl 1036.62108 [2] Croux, K.; Veraverbeke, N., Non-parametric estimators for the probability of ruin, Insurance Math. Econom., 9, 127-130 (1990) · Zbl 0711.62096 [3] Mnatsakanov, R.; Ruymgaart, L. L.; Ruymgaart, F. H., Nonparametric estimation of ruin probabilities given a random sample of claims, Math. Methods Statist., 17, 1, 35-43 (2008) · Zbl 1282.62080 [4] Pitts, S. M., Nonparametric estimation of compound distributions with applications in insurance, Ann. Inst. Statist. Math., 46, 3, 537-555 (1994) · Zbl 0817.62024 [5] Politis, K., Semiparametric estimation for non-ruin probabilities, Scand. Actuar. J., 2003, 1, 75-96 (2003) · Zbl 1092.91054 [6] Zhang, Z.; Yang, H., Nonparametric estimate for the ruin probability in a Lévy risk model with low-frequency observation, Insurance Math. Econom., 59, 168-177 (2014) · Zbl 1306.91088 [7] Frees, EW., Nonparametric estimation of the probability of ruin, Astin Bull., 16, 81-90 (1986) [8] Hipp, C., Estimators and bootstrap confidence intervals for ruin probabilities, Astin Bull., 19, 57-70 (1989) [9] Shimizu, Y., Non-parametric estimation of the Gerber-Shiu function for the Wiener-Poisson risk model, Scand. Actuar. J., 2012, 1, 56-69 (2012) · Zbl 1277.62096 [10] Morales, M., On the expected discounted penalty function for a perturbed risk process driven by a subordinator, Insur.: Math. Econ., 40, 2, 293-301 (2007) · Zbl 1130.91032 [11] Vapnik, V., Estimation of Dependences Based on Empirical Data (2006), Springer: Springer New York [12] Chauveau, D. E.; Vanrooij, A. C.M.; Ruymgaart, F. H., Regularized inversion of noisy Laplace transforms, Adv. in Appl. Math., 15, 2, 186-201 (1994) · Zbl 0806.65136 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.