IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v144y2022icp72-84.html
   My bibliography  Save this article

Ruin probabilities for a Sparre Andersen model with investments

Author

Listed:
  • Eberlein, Ernst
  • Kabanov, Yuri
  • Schmidt, Thorsten

Abstract

We study a Sparre Andersen model in which the business activity of the company is described by a compound renewal process with drift assuming that the capital reserves are invested in a risky asset. The price of the latter is assumed to evolve according to a geometric Lévy process. We prove that the asymptotic behavior of the ruin probability depends to a large extent only on the properties of the price process.

Suggested Citation

  • Eberlein, Ernst & Kabanov, Yuri & Schmidt, Thorsten, 2022. "Ruin probabilities for a Sparre Andersen model with investments," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 72-84.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:72-84
    DOI: 10.1016/j.spa.2021.10.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414921001800
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2021.10.011?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. Anna Frolova & Serguei Pergamenshchikov & Yuri Kabanov, 2002. "In the insurance business risky investments are dangerous," Finance and Stochastics, Springer, vol. 6(2), pages 227-235.
    2. Paulsen, Jostein, 1998. "Sharp conditions for certain ruin in a risk process with stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 135-148, June.
    3. Albrecher, Hansjoerg & Constantinescu, Corina & Thomann, Enrique, 2012. "Asymptotic results for renewal risk models with risky investments," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3767-3789.
    4. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    5. Yuri Kabanov & Serguei Pergamenshchikov, 2020. "Ruin probabilities for a Lévy-driven generalised Ornstein–Uhlenbeck process," Finance and Stochastics, Springer, vol. 24(1), pages 39-69, January.
    6. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuri Kabanov & Platon Promyslov, 2023. "Ruin probabilities for a Sparre Andersen model with investments: the case of annuity payments," Finance and Stochastics, Springer, vol. 27(4), pages 887-902, October.
    2. Yuri Kabanov & Sergey Pergamenshchikov, 2022. "On ruin probabilities with investments in a risky asset with a regime-switching price," Finance and Stochastics, Springer, vol. 26(4), pages 877-897, October.

    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. Yuri Kabanov & Platon Promyslov, 2023. "Ruin probabilities for a Sparre Andersen model with investments: the case of annuity payments," Finance and Stochastics, Springer, vol. 27(4), pages 887-902, October.
    2. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    3. Yuri Kabanov & Serguei Pergamenshchikov, 2020. "Ruin probabilities for a Lévy-driven generalised Ornstein–Uhlenbeck process," Finance and Stochastics, Springer, vol. 24(1), pages 39-69, January.
    4. Jing Wang & Zbigniew Palmowski & Corina Constantinescu, 2021. "How Much We Gain by Surplus-Dependent Premiums—Asymptotic Analysis of Ruin Probability," Risks, MDPI, vol. 9(9), pages 1-17, August.
    5. Paulsen, Jostein & Kasozi, Juma & Steigen, Andreas, 2005. "A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 399-420, June.
    6. David Maher, 2005. "A Note on the Ruin Problem with Risky Investments," Papers math/0506127, arXiv.org, revised Jul 2005.
    7. Nyrhinen, Harri, 2007. "Convex large deviation rate functions under mixtures of linear transformations, with an application to ruin theory," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 947-959, July.
    8. Kostadinova, Radostina, 2007. "Optimal investment for insurers when the stock price follows an exponential Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 250-263, September.
    9. Yin, Chuancun & Wen, Yuzhen, 2013. "An extension of Paulsen–Gjessing’s risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 469-476.
    10. Tang, Qihe & Wang, Guojing & Yuen, Kam C., 2010. "Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 362-370, April.
    11. Xiong, Sheng & Yang, Wei-Shih, 2011. "Ruin probability in the Cramér-Lundberg model with risky investments," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1125-1137, May.
    12. Klüppelberg, Claudia & Kostadinova, Radostina, 2008. "Integrated insurance risk models with exponential Lévy investment," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 560-577, April.
    13. Azcue, Pablo & Muler, Nora, 2009. "Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 26-34, February.
    14. Grandits, Peter, 2004. "A Karamata-type theorem and ruin probabilities for an insurer investing proportionally in the stock market," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 297-305, April.
    15. Yuri Kabanov & Sergey Pergamenshchikov, 2022. "On ruin probabilities with investments in a risky asset with a regime-switching price," Finance and Stochastics, Springer, vol. 26(4), pages 877-897, October.
    16. Paulsen, Jostein, 1998. "Ruin theory with compounding assets -- a survey," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 3-16, May.
    17. Yuchao Dong & Jérôme Spielmann, 2020. "Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory," Post-Print hal-02170829, HAL.
    18. Nyrhinen, Harri, 2001. "Finite and infinite time ruin probabilities in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 265-285, April.
    19. Nyrhinen, Harri, 1999. "On the ruin probabilities in a general economic environment," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 319-330, October.
    20. Yuchao Dong & J'er^ome Spielmann, 2019. "Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory," Papers 1907.01828, arXiv.org, revised Feb 2020.

    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:spapps:v:144:y:2022:i:c:p:72-84. 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/wps/find/journaldescription.cws_home/505572/description#description .

    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.