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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 3–20 (Mi tvp2954)  

This article is cited in 9 scientific papers (total in 9 papers)

Nonparametric estimation of the ruin probability for generalized risk processes

V. E. Bening, V. Yu. Korolev

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: In this paper we construct a statistical estimator of the ruin probability for a generalized risk process characterized by the stochastic character of the premium rate and of the intensity of insurance payments. The asymptotic properties of the proposed estimator are considered. Algorithms are proposed for the construction of approximate nonparametric confidence intervals for the ruin probability.

Keywords: risk process, generalized risk process, ruin probability, random sequences with random indices, unbiasedness, consistency, confidence intervals.

DOI: https://doi.org/10.4213/tvp2954

Full text: PDF file (1669 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 1–16

Bibliographic databases:

Received: 08.04.1999

Citation: V. E. Bening, V. Yu. Korolev, “Nonparametric estimation of the ruin probability for generalized risk processes”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 3–20; Theory Probab. Appl., 47:1 (2003), 1–16

Citation in format AMSBIB
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\by V.~E.~Bening, V.~Yu.~Korolev
\paper Nonparametric estimation of the ruin probability for generalized
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\jour Teor. Veroyatnost. i Primenen.
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\pages 3--20
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\zmath{https://zbmath.org/?q=an:1036.62108}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 1--16
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Shimizu Ya., “Non-Parametric Estimation of the Gerber-Shiu Function for the Wiener-Poisson Risk Model”, Scand. Actuar. J., 2012, no. 1, 56–69  crossref  mathscinet  zmath  isi  elib  scopus
    2. Feng R., Shimizu Ya., “On a Generalization From Ruin to Default in a Lévy Insurance Risk Model”, Methodol. Comput. Appl. Probab., 15:4 (2013), 773–802  crossref  mathscinet  zmath  isi  scopus
    3. Gordienko E., Vazquez-Ortega P., “Simple Continuity Inequalities for Ruin Probability in the Classical Risk Model”, Astin Bull., 46:3 (2016), 799–814  crossref  mathscinet  isi  scopus
    4. Shiraishi H., “Review of statistical actuarial risk modelling”, Cogent Math., 3 (2016), 1123945  crossref  mathscinet  isi
    5. Mishura Y., Ragulina O., “Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach”, Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach, Iste Ltd, 2016, 1–260  mathscinet  zmath  isi
    6. Oshime T., Shimizu Ya., “Parametric Inference For Ruin Probability in the Classical Risk Model”, Stat. Probab. Lett., 133 (2018), 28–37  crossref  mathscinet  zmath  isi  scopus
    7. Cai Ch., Chen N., You H., “Nonparametric Estimation For a Spectrally Negative Levy Risk Process Based on Low-Frequency Observation”, J. Comput. Appl. Math., 328 (2018), 432–442  crossref  mathscinet  zmath  isi  scopus
    8. Cai Ch., Guo J., You H., “Non-Parametric Estimation For a Pure-Jump Levy Process”, Ann. Actuar. Sci., 12:2 (2018), 338–349  crossref  mathscinet  isi
    9. You H., Gao Yu., “Non-Parametric Threshold Estimation For the Wiener-Poisson Risk Model”, Mathematics, 7:6 (2019), 506  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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