Estimation of ruin probability for binomially distributed number of $\varphi$-sub-Gaussian claims

Authors

DOI:

https://doi.org/10.17721/1812-5409.2022/2.2

Keywords:

binomial distribution, φ-sub-Gaussian random variables, ruin probability

Abstract

In this paper, we study the properties of a risk process, formed by binomial sum of $\varphi$-sub-Gaussian risks. Estimates for probability of exceeding a monotone increasing continuous curve by such a sum are obtained. In particular, the ruin probability estimate is derived for the risk process in case of linearly incoming premiums.

Pages of the article in the issue: 20 - 27

Language of the article: Ukrainian

Author Biography

Rostyslav Yamnenko, Taras Shevchenko National University of Kyiv

Кафедра теорії ймовірності, статистики і актуарної математики, доцент

References

VASYLYK, O. I., KOZACHENKO, YU. V., YAMNENKO, R. E. (2008) $varphi $-sub-Gaussian random process, Kyiv: Vydavnycho-Poligrafichnyi Tsentr ``Kyivskyi Universytet'', 231 p. (In Ukrainian)

BULDYGIN, V. V., KOZACHENKO, YU. V. (2000) Metric Characterization of Random Variables and Random Processes. American Mathematical Society, Providence, RI, 257 p.

GIULIANO ANTONINI, R., KOZACHENKO, YU. V., NIKITINA, T. (2003) Space of $varphi$-sub-Gaussian random variables. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 27, p.92-124.

KOZACHENKO, YU., YAMNENKO, R., VASYLYK, O. (2005) Upper estimate of overrunning by $Sub_varphi(Omega)$ random process the level specified by continuous function. Random Oper. Stoch. Equ. 13, no. 2, p.111-128.

YAMNENKO, R., VASYLYK O. (2007) Random process from the class $V(varphi,psi)$: Exceeding a curve. Theory of Stochastic Processes. Vol.13 (29), no.4, p. 219-232.

VASYLYK O., YAMNENKO, R. (2007) Some properties of random Poisson sums with $varphi$-sub-Gaussian terms. Prykl. Stat., Aktuarna Finans. Mat. Vol.1., p. 133-148.

SAIENKO M.I., YAMNENKO R.E. (2013) Sub-Gaussian risk processes with dependent moments of claims incoming and contracts signing. Nauk. visnyk Uzngorod. Un-ty. Vol.24, iss.2, p. 176-184.

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Published

2022-10-12

How to Cite

Ямненко, Р., & Ламін, А. (2022). Estimation of ruin probability for binomially distributed number of $\varphi$-sub-Gaussian claims. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (2), 20–27. https://doi.org/10.17721/1812-5409.2022/2.2

Issue

Section

Algebra, Geometry and Probability Theory