IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v118y2024icp142-156.html
   My bibliography  Save this article

Probabilistic approach to risk processes with level-dependent premium rate

Author

Listed:
  • Denisov, Denis
  • Gotthardt, Niklas
  • Korshunov, Dmitry
  • Wachtel, Vitali

Abstract

We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift.

Suggested Citation

  • Denisov, Denis & Gotthardt, Niklas & Korshunov, Dmitry & Wachtel, Vitali, 2024. "Probabilistic approach to risk processes with level-dependent premium rate," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 142-156.
    • Handle: RePEc:eee:insuma:v:118:y:2024:i:c:p:142-156
    DOI: 10.1016/j.insmatheco.2024.06.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668724000726
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2024.06.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Czarna, Irmina & Pérez, José-Luis & Rolski, Tomasz & Yamazaki, Kazutoshi, 2019. "Fluctuation theory for level-dependent Lévy risk processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5406-5449.
    2. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums," Papers 1604.06892, arXiv.org.
    3. Denisov, Denis & Korshunov, Dmitry & Wachtel, Vitali, 2013. "Potential analysis for positive recurrent Markov chains with asymptotically zero drift: Power-type asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3027-3051.
    4. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 723-742, February.
    5. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ewa Marciniak & Zbigniew Palmowski, 2018. "On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 533-552, November.
    2. Linlin Tian & Lihua Bai & Junyi Guo, 2020. "Optimal Singular Dividend Problem Under the Sparre Andersen Model," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 603-626, February.
    3. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums," Papers 1605.04584, arXiv.org.
    4. Gordienko, E. & Vázquez-Ortega, P., 2018. "Continuity inequalities for multidimensional renewal risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 48-54.
    5. Osatakul, Dhiti & Li, Shuanming & Wu, Xueyuan, 2023. "Discrete-time risk models with surplus-dependent premium corrections," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    6. Florin Avram & Jose-Luis Perez-Garmendia, 2019. "A Review of First-Passage Theory for the Segerdahl-Tichy Risk Process and Open Problems," Risks, MDPI, vol. 7(4), pages 1-21, November.
    7. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    8. Grandell, Jan, 2000. "Simple approximations of ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 157-173, May.
    9. S. Pitts, 1994. "Nonparametric estimation of compound distributions with applications in insurance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 537-555, September.
    10. Julien Trufin & Stéphane Loisel, 2013. "Ultimate ruin probability in discrete time with Bühlmann credibility premium adjustments," Post-Print hal-00426790, HAL.
    11. Yuen, Kam C. & Wang, Guojing & Ng, Kai W., 2004. "Ruin probabilities for a risk process with stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 259-274, April.
    12. Tang, Qihe & Wei, Li, 2010. "Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 19-31, February.
    13. Vaios Dermitzakis & Konstadinos Politis, 2011. "Asymptotics for the Moments of the Time to Ruin for the Compound Poisson Model Perturbed by Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 749-761, December.
    14. J. Cerda-Hernandez & A. Sikov & A. Ramos, 2022. "An optimal investment strategy aimed at maximizing the expected utility across all intermediate capital levels," Papers 2207.02947, arXiv.org, revised Jun 2024.
    15. Albrecher, Hansjörg & Kortschak, Dominik, 2009. "On ruin probability and aggregate claim representations for Pareto claim size distributions," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 362-373, December.
    16. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    17. Toshiro Watanabe & Kouji Yamamuro, 2010. "Local Subexponentiality and Self-decomposability," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1039-1067, December.
    18. Ramsay, Colin M., 2003. "A solution to the ruin problem for Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 109-116, August.
    19. Wang, Dingcheng & Chen, Pingyan & Su, Chun, 2007. "The supremum of random walk with negatively associated and heavy-tailed steps," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1403-1412, July.
    20. Baltru-nas, Aleksandras, 2005. "Second order behaviour of ruin probabilities in the case of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 485-498, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:118:y:2024:i:c:p:142-156. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.