×

Approximations in the problem of level crossing by a compound renewal process. (English. Russian original) Zbl 1420.60114

Dokl. Math. 98, No. 3, 622-625 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 483, No. 5, 488-491 (2018).
Summary: The classical problem of level crossing by a compound renewal process is considered, which has been extensively studied and has various applications. For the distribution of the first level crossing time, a new approximation is proposed, which is valid under minimal conditions and is obtained by applying a new method. It has a number of advantages over previously known approximations.

MSC:

60K15 Markov renewal processes, semi-Markov processes
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Asmussen, S., No article title, Scand. Actuarial J., 1984, 31-57 (1984) · Zbl 0568.62092
[2] S. Asmussen and H. Albrecher, Ruin Probabilities (World Scientific, Singapore, 2010). · Zbl 1247.91080
[3] Bahr, B., No article title, Scand. Actuarial J., 1974, 190-204 (1974) · Zbl 0321.62103
[4] Borovkov, K.; Dickson, D. C. M., No article title, Insurance Math. Econ., 42, 1104-1108 (2008) · Zbl 1141.91486
[5] Drekic, S.; Willmot, G. E., No article title, ASTIN Bull., 33, 11-21 (2003)
[6] Garcia, J. M. A., No article title, ASTIN Bull., 35, 113-130 (2005)
[7] Malinovskii, V. K., No article title, Insurance Math. Econ., 22, 123-138 (1998) · Zbl 0907.90099
[8] V. K. Malinovskii, “On the time of first level crossing and inverse Gaussian distribution,” (2017). https://doi.org/arxiv.org/pdf/1708.08665.pdf.
[9] V. K. Malinovskii, “Generalized inverse Gaussian distributions and the time of first level crossing” (2017). https://doi.org/arxiv.org/pdf/1708.08671.pdf.
[10] V. K. Malinovskii and K. V. Malinovskii, “On approximations for the distribution of first level crossing time” (2017). https://doi.org/arxiv.org/pdf/1708.08678.pdf. · Zbl 0864.62070
[11] Teugels, J. L., No article title, Insurance Math. Econ., 1, 163-175 (1982) · Zbl 0508.62088
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.