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An Insurance Company Model with Random Premiums and Claims. / Товстик, Татьяна Михайловна; Булгакова, Дарья Сергеевна.

In: Vestnik St. Petersburg University: Mathematics, Vol. 58, No. 1, 01.03.2025, p. 79–91 .

Research output: Contribution to journal › Article › peer-review

Harvard

Товстик, ТМ & Булгакова, ДС 2025, 'An Insurance Company Model with Random Premiums and Claims', Vestnik St. Petersburg University: Mathematics, vol. 58, no. 1, pp. 79–91 . https://doi.org/10.1134/s1063454125700098

APA

Товстик, Т. М., & Булгакова, Д. С. (2025). An Insurance Company Model with Random Premiums and Claims. Vestnik St. Petersburg University: Mathematics, 58(1), 79–91 . https://doi.org/10.1134/s1063454125700098

Vancouver

Товстик ТМ, Булгакова ДС. An Insurance Company Model with Random Premiums and Claims. Vestnik St. Petersburg University: Mathematics. 2025 Mar 1;58(1):79–91 . https://doi.org/10.1134/s1063454125700098

Author

Товстик, Татьяна Михайловна ; Булгакова, Дарья Сергеевна. / An Insurance Company Model with Random Premiums and Claims. In: Vestnik St. Petersburg University: Mathematics. 2025 ; Vol. 58, No. 1. pp. 79–91 .

BibTeX

@article{fde9e162c2b84c42bcd668d544977fcd,
title = "An Insurance Company Model with Random Premiums and Claims",
abstract = "This article considers the stochastic Cramer–Lundberg model, in which premiums and insurance compensations (claims) are random and independent. Premiums are equally distributed and obey the exponential law. Claims are also equally distributed according to the exponential law, which has a positive shift from the origin. A homogeneous Poisson process is introduced, whose jumps are interpreted as the moments of premium receipt, while the intensity corresponds to the average number of premiums per year. The Poisson process does not depend on the random variables representing premiums and insurance compensations. Insurance events occur at the same times as premiums are received, but with less intensity. The probabilities of a company{\textquoteright}s ruin at the first three times of the appearance of claims are found, and a scheme for sequentially calculating the probabilities of ruin at the times of receipt of insurance events is given. Examples are given.",
keywords = "ruin probability, risk model, stochastic insurance company model, exponential distribution with a shift in insurance claims, exponential distribution with a shift in insurance claims, risk model, ruin probability, stochastic insurance company model",
author = "Товстик, {Татьяна Михайловна} and Булгакова, {Дарья Сергеевна}",
note = "Tovstik, T.M., Bulgakova, D.S. An Insurance Company Model with Random Premiums and Claims. Vestnik St.Petersb. Univ.Math. 58, 79–91 (2025). https://doi.org/10.1134/S1063454125700098",
year = "2025",
month = mar,
day = "1",
doi = "10.1134/s1063454125700098",
language = "English",
volume = "58",
pages = "79–91 ",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - An Insurance Company Model with Random Premiums and Claims

AU - Товстик, Татьяна Михайловна

AU - Булгакова, Дарья Сергеевна

N1 - Tovstik, T.M., Bulgakova, D.S. An Insurance Company Model with Random Premiums and Claims. Vestnik St.Petersb. Univ.Math. 58, 79–91 (2025). https://doi.org/10.1134/S1063454125700098

PY - 2025/3/1

Y1 - 2025/3/1

N2 - This article considers the stochastic Cramer–Lundberg model, in which premiums and insurance compensations (claims) are random and independent. Premiums are equally distributed and obey the exponential law. Claims are also equally distributed according to the exponential law, which has a positive shift from the origin. A homogeneous Poisson process is introduced, whose jumps are interpreted as the moments of premium receipt, while the intensity corresponds to the average number of premiums per year. The Poisson process does not depend on the random variables representing premiums and insurance compensations. Insurance events occur at the same times as premiums are received, but with less intensity. The probabilities of a company’s ruin at the first three times of the appearance of claims are found, and a scheme for sequentially calculating the probabilities of ruin at the times of receipt of insurance events is given. Examples are given.

AB - This article considers the stochastic Cramer–Lundberg model, in which premiums and insurance compensations (claims) are random and independent. Premiums are equally distributed and obey the exponential law. Claims are also equally distributed according to the exponential law, which has a positive shift from the origin. A homogeneous Poisson process is introduced, whose jumps are interpreted as the moments of premium receipt, while the intensity corresponds to the average number of premiums per year. The Poisson process does not depend on the random variables representing premiums and insurance compensations. Insurance events occur at the same times as premiums are received, but with less intensity. The probabilities of a company’s ruin at the first three times of the appearance of claims are found, and a scheme for sequentially calculating the probabilities of ruin at the times of receipt of insurance events is given. Examples are given.

KW - ruin probability

KW - risk model

KW - stochastic insurance company model

KW - exponential distribution with a shift in insurance claims

KW - exponential distribution with a shift in insurance claims

KW - risk model

KW - ruin probability

KW - stochastic insurance company model

UR - https://www.mendeley.com/catalogue/0c84d8e2-c657-348f-9d60-15ecbe4affd6/

U2 - 10.1134/s1063454125700098

DO - 10.1134/s1063454125700098

M3 - Article

VL - 58

SP - 79

EP - 91

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 135972012