IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i5-6p427-436.html
   My bibliography  Save this article

On the classical risk model with credit and debit interests under absolute ruin

Author

Listed:
  • Wang, Chunwei
  • Yin, Chuancun
  • Li, Erqiang

Abstract

In this paper, we consider the dividend payments in a compound Poisson risk model with credit and debit interests under absolute ruin. We first obtain the integro-differential equations satisfied by the moment generating function and moments of the discounted aggregate dividend payments. Secondly, applying these results, we get the explicit expressions of them for exponential claims. Then, we give the numerical analysis of the optimal dividend barrier and the expected discounted aggregate dividend payments which are influenced by the debit and credit interests. Finally, we find the integro-differential equations satisfied by the Laplace transform of absolute ruin time and give its explicit expressions when the claim sizes are exponentially distributed.

Suggested Citation

  • Wang, Chunwei & Yin, Chuancun & Li, Erqiang, 2010. "On the classical risk model with credit and debit interests under absolute ruin," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 427-436, March.
  • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:427-436
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00444-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gerber, Hans U. & Shiu, Elias S.W. & Smith, Nathaniel, 2008. "Methods for estimating the optimal dividend barrier and the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 243-254, February.
    2. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 324-334, October.
    3. Hans Gerber & Hailiang Yang, 2007. "Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 159-169.
    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. Li, Manman & Liu, Zaiming, 2012. "Regulated absolute ruin problem with interest structure and linear dividend barrier," Economic Modelling, Elsevier, vol. 29(5), pages 1786-1792.
    2. Li, Shuanming & Lu, Yi, 2013. "On the generalized Gerber–Shiu function for surplus processes with interest," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 127-134.
    3. Yunyun Wang & Wenguang Yu & Yujuan Huang & Xinliang Yu & Hongli Fan, 2019. "Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income," Mathematics, MDPI, vol. 7(3), pages 1-25, March.
    4. Yu, Wenguang, 2013. "Some results on absolute ruin in the perturbed insurance risk model with investment and debit interests," Economic Modelling, Elsevier, vol. 31(C), pages 625-634.

    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. Yuen, Kam-Chuen & Zhou, Ming & Guo, Junyi, 2008. "On a risk model with debit interest and dividend payments," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2426-2432, October.
    2. Li, Manman & Liu, Zaiming, 2012. "Regulated absolute ruin problem with interest structure and linear dividend barrier," Economic Modelling, Elsevier, vol. 29(5), pages 1786-1792.
    3. Chunwei Wang & Chuancun Yin, 2009. "Dividend payments in the classical risk model under absolute ruin with debit interest," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 247-262, May.
    4. Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2022. "Optimal dividends under Markov-modulated bankruptcy level," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 146-172.
    5. Liang, Zongxia & Long, Mingsi, 2015. "Minimization of absolute ruin probability under negative correlation assumption," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 247-258.
    6. Ramsden, Lewis & Papaioannou, Apostolos D., 2019. "Ruin probabilities under capital constraints," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 273-282.
    7. Liang, Xiaoqing & Liang, Zhibin & Young, Virginia R., 2020. "Optimal reinsurance under the mean–variance premium principle to minimize the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 128-146.
    8. Yang, Hu & Zhang, Zhimin, 2008. "Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 984-991, June.
    9. Cheung, Eric C.K., 2011. "A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 384-397, May.
    10. 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.
    11. Li, Shuanming & Lu, Yi, 2013. "On the generalized Gerber–Shiu function for surplus processes with interest," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 127-134.
    12. Florin Avram & Andras Horváth & Serge Provost & Ulyses Solon, 2019. "On the Padé and Laguerre–Tricomi–Weeks Moments Based Approximations of the Scale Function W and of the Optimal Dividends Barrier for Spectrally Negative Lévy Risk Processes," Risks, MDPI, vol. 7(4), pages 1-24, December.
    13. Landriault, David, 2008. "Constant dividend barrier in a risk model with interclaim-dependent claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 31-38, February.
    14. Gerber, Hans U. & Smith, Nathaniel, 2008. "Optimal dividends with incomplete information in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 227-233, October.
    15. Maite Teresa Marmol Jimenez & M. Mercedes Claramunt Bielsa, 2006. "Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier," Working Papers in Economics 157, Universitat de Barcelona. Espai de Recerca en Economia.
    16. Chuancun Yin & Chunwei Wang, 2010. "The Perturbed Compound Poisson Risk Process with Investment and Debit Interest," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 391-413, September.
    17. Luo, Shangzhen & Taksar, Michael, 2011. "On absolute ruin minimization under a diffusion approximation model," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 123-133, January.
    18. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    19. 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.
    20. Kim, Bara & Kim, Hwa-Sung & Kim, Jeongsim, 2008. "A risk model with paying dividends and random environment," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 717-726, April.

    More about this item

    Statistics

    Access and download statistics

    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:stapro:v:80:y:2010:i:5-6:p:427-436. 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/622892/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.