IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v17y2015i4d10.1007_s11009-014-9418-3.html
   My bibliography  Save this article

Discrete-time Insurance Model with Capital Injections and Reinsurance

Author

Listed:
  • Ekaterina Bulinskaya

    (Lomonosov Moscow State University)

  • Julia Gusak

    (Lomonosov Moscow State University)

  • Anastasia Muromskaya

    (Lomonosov Moscow State University)

Abstract

A periodic-review insurance model is considered under the following assumptions. In order to avoid ruin the insurer maintains the company surplus above a chosen level a by capital injections at the end of each period. One-period insurance claims form a sequence of independent identically distributed nonnegative random variables with finite mean. A nonproportional reinsurance is applied for minimization of total expected discounted injections during a given planning horizon of n periods. Insurance and reinsurance premiums are calculated using the expected value principle. Optimal reinsurance strategy is established. Numerical results illustrating the theoretical ones are provided for three claims distributions.

Suggested Citation

  • Ekaterina Bulinskaya & Julia Gusak & Anastasia Muromskaya, 2015. "Discrete-time Insurance Model with Capital Injections and Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 899-914, December.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-014-9418-3
    DOI: 10.1007/s11009-014-9418-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-014-9418-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-014-9418-3?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. Hojgaard, Bjarne & Taksar, Michael, 1998. "Optimal proportional reinsurance policies for diffusion models with transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 41-51, May.
    2. Diasparra, M. & Romera, R., 2010. "Inequalities for the ruin probability in a controlled discrete-time risk process," European Journal of Operational Research, Elsevier, vol. 204(3), pages 496-504, August.
    3. Wei, Xiao & Hu, Yijun, 2008. "Ruin probabilities for discrete time risk models with stochastic rates of interest," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 707-715, April.
    4. Dickson, David C.M. & Waters, Howard R., 2004. "Some Optimal Dividends Problems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 49-74, May.
    5. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
    6. Dickson, David C.M. & Waters, Howard R., 2006. "Optimal Dynamic Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 415-432, November.
    7. Wai-Sum Chan & Lianzeng Zhang, 2006. "Direct Derivation of Finite-Time Ruin Probabilities in the Discrete Risk Model with Exponential or Geometric Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 269-279.
    8. Hipp, Christian & Vogt, Michael, 2003. "Optimal Dynamic XL Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 193-207, November.
    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. Ekaterina Bulinskaya & Boris Shigida, 2021. "Discrete-Time Model of Company Capital Dynamics with Investment of a Certain Part of Surplus in a Non-Risky Asset for a Fixed Period," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 103-121, March.
    2. Abouzar Bazyari, 2023. "On the Ruin Probabilities in a Discrete Time Insurance Risk Process with Capital Injections and Reinsurance," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1623-1650, August.

    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. Anna Castañer & M. Claramunt & Maite Mármol, 2012. "Ruin probability and time of ruin with a proportional reinsurance threshold strategy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 614-638, October.
    2. Ekaterina Bulinskaya & Boris Shigida, 2021. "Discrete-Time Model of Company Capital Dynamics with Investment of a Certain Part of Surplus in a Non-Risky Asset for a Fixed Period," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 103-121, March.
    3. Tan, Ken Seng & Wei, Pengyu & Wei, Wei & Zhuang, Sheng Chao, 2020. "Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle," European Journal of Operational Research, Elsevier, vol. 282(1), pages 345-362.
    4. Arian Cani & Stefan Thonhauser, 2017. "An optimal reinsurance problem in the Cramér–Lundberg model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 179-205, April.
    5. Cerqueti, Roy & Foschi, Rachele & Spizzichino, Fabio, 2009. "A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 59-64, August.
    6. Muhsin Tamturk & Sergey Utev, 2019. "Optimal Reinsurance via Dirac-Feynman Approach," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 647-659, June.
    7. Chonghu Guan & Zuo Quan Xu & Rui Zhou, 2020. "Dynamic optimal reinsurance and dividend-payout in finite time horizon," Papers 2008.00391, arXiv.org, revised Jun 2022.
    8. Christian Hipp, 2018. "Company Value with Ruin Constraint in Lundberg Models," Risks, MDPI, vol. 6(3), pages 1-15, July.
    9. Zhang, Nan & Jin, Zhuo & Li, Shuanming & Chen, Ping, 2016. "Optimal reinsurance under dynamic VaR constraint," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 232-243.
    10. Zhang, Aili & Li, Shuanming & Wang, Wenyuan, 2023. "A scale function based approach for solving integral-differential equations in insurance risk models," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    11. Liang, Zhibin & Young, Virginia R., 2012. "Dividends and reinsurance under a penalty for ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 437-445.
    12. Castañer, A. & Claramunt, M.M. & Lefèvre, C., 2013. "Survival probabilities in bivariate risk models, with application to reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 632-642.
    13. Anna Castañer & M.Mercè Claramunt & Maite Mármol, 2014. "Some optimization and decision problems in proportional reinsurance," UB School of Economics Working Papers 2014/310, University of Barcelona School of Economics.
    14. Benjamin Avanzi & Hayden Lau & Bernard Wong, 2020. "On the optimality of joint periodic and extraordinary dividend strategies," Papers 2006.00717, arXiv.org, revised Dec 2020.
    15. Avanzi, Benjamin & Lau, Hayden & Wong, Bernard, 2021. "On the optimality of joint periodic and extraordinary dividend strategies," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1189-1210.
    16. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
    17. Xu, Ran & Woo, Jae-Kyung, 2020. "Optimal dividend and capital injection strategy with a penalty payment at ruin: Restricted dividend payments," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 1-16.
    18. Zhou, Zhou & Jin, Zhuo, 2020. "Optimal equilibrium barrier strategies for time-inconsistent dividend problems in discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 100-108.
    19. Mohamed Mnif, 2010. "Optimal insurance demand under marked point processes shocks: a dynamic programming duality approach," Papers 1008.5058, arXiv.org.
    20. Li, Shuanming & Dickson, David C.M., 2006. "The maximum surplus before ruin in an Erlang(n) risk process and related problems," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 529-539, 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:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-014-9418-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.