Skip to main content
SpringerLink
Log in

A Mathematical Model of Insurer Bankruptcy on a Finite Time Interval

  • I. MATHEMATICAL MODELING
  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

A discrete-time model is proposed for an insurance company with a Poisson stream of new insurance policies added to the portfolio and a mixed Poisson stream of insurance claims. Recursive formulas are derived for the first three moments of the risk surplus and a lower bound is obtained for the probability that the surplus remains positive on a given time interval.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Bowers, H. Gerber, and others, Actuarial Mathematics [Russian translation], Yanus-K, Moscow (2001).

    Google Scholar 

  2. E. Sparre Andersen, “On the collective theory of risk in case of contagion between the claims,” Trans. XVth International Congress of Actuaries, II (1957), pp. 219–229.

  3. J. Grandell, Aspects of Risk Theory, Springer, New York (1991).

    Book  Google Scholar 

  4. V. Yu. Korolev, V. E. Bening, and S. Ya. Shorgin, Mathematical Foundations of Risk Theory [in Russian], Fizmatlit, Moscow (2011).

  5. V. V. Kalashnikov and A. A. Konstantinidis, “Ruin probability,” Funtamental’naya i Prikladnaya Matematika, 2, No. 4, 1005–1100 (1996).

    MathSciNet  MATH  Google Scholar 

  6. Q. Tang and G. Tsitsiashvili, “Finite and infinite time ruin probabilities in the presence of stochastic returns on investments,” Advances in Applied Probability, 36, No. 4, 1278–1299 (2004).

    Article  MathSciNet  Google Scholar 

  7. Y. Yang, T. Jiang, K. Wang, and K. Yuen, “Interplay of financial and insurance risks in dependent discrete-time risk models,” Statistics & Probability Letters, 162, 108752 (July 2020).

  8. T. A. Belkina, N. B. Konyukhova, and S. V. Kurochkin, “Singular initial- and boundary-value problems for integro-differential equations in dynamic insurance models with investments,” Sovremennaya Matematika. Fundamental’nye Napravleniya, 53, 5–29 (2014).

    Google Scholar 

  9. T. A. Belkina, N. B. Konyukhova, and B. V. Slavko, “Risk-free investments and their comparison with simple risk strategy in the pension insurance model: solution of singular problems for integro-differential equations,” Zh. Vychisl. Mat. i Matem. Fiz., 60, No. 10, 1676–1696 (2020).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    A. A. Belolipetskiy

  2. Dorodnitsyn Computational Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences (FITs IU RAN), Moscow, Russia

    A. A. Belolipetskiy

  3. Moscow Institute of Physics and Technology (Public Research University), Moscow, Russia

    A. A. Belolipetskiy & A. A. Sychev

Authors
  1. A. A. Belolipetskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Sychev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Belolipetskiy.

Additional information

Translated from Prikladnaya Matematika i Informatika, No. 67, 2021, pp. 4–18.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belolipetskiy, A.A., Sychev, A.A. A Mathematical Model of Insurer Bankruptcy on a Finite Time Interval. Comput Math Model 32, 259–275 (2021). https://doi.org/10.1007/s10598-021-09530-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10598-021-09530-1

Keywords

Search

Navigation