IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v77y2007i8p761-768.html
   My bibliography  Save this article

Ruin problems in risk models with dependent rates of interest

Author

Listed:
  • Gao, Qi-bing
  • Wu, Yao-hua
  • Zhu, Chun-hua
  • Wei, Guang-hua

Abstract

In this paper, we consider ruin problems in two generalized risk models. The effects of timing of payments and interest on the ruin problems in the models are studied. The rates of interest {In,n=1,2,...} are assumed to have an autoregressive structure. We obtain the recursive formulas of penalty functions which give a unified treatment to ruin quantities including the distribution of surplus immediately before ruin and the deficit at ruin, etc. Furthermore, we consider the probability properties of the duration of ruin, which are used to describe the severity of ruin.

Suggested Citation

  • Gao, Qi-bing & Wu, Yao-hua & Zhu, Chun-hua & Wei, Guang-hua, 2007. "Ruin problems in risk models with dependent rates of interest," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 761-768, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:8:p:761-768
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(06)00348-8
    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. Cai, Jun & Dickson, David C. M., 2002. "On the expected discounted penalty function at ruin of a surplus process with interest," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 389-404, June.
    2. Cai, Jun, 2004. "Ruin probabilities and penalty functions with stochastic rates of interest," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 53-78, July.
    3. Gerber, Hans U. & Shiu, Elias S. W., 1997. "The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 129-137, 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. Xin Deng & Xuejun Wang, 2020. "An exponential inequality and its application to M estimators in multiple linear models," Statistical Papers, Springer, vol. 61(4), pages 1607-1627, August.
    2. Wenhao Li & Bolong Wang & Tianxiang Shen & Ronghua Zhu & Dehui Wang, 2017. "Research on ruin probability of risk model based on AR(1) series," Papers 1710.10692, arXiv.org.

    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. Wu, Rong & Wang, Guojing & Zhang, Chunsheng, 2005. "On a joint distribution for the risk process with constant interest force," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 365-374, June.
    2. Biffis, Enrico & Kyprianou, Andreas E., 2010. "A note on scale functions and the time value of ruin for Lévy insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 85-91, February.
    3. Jun Cai & Runhuan Feng & Gordon E. Willmot, 2009. "The Compound Poisson Surplus Model with Interest and Liquid Reserves: Analysis of the Gerber–Shiu Discounted Penalty Function," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 401-423, September.
    4. Tan, Jiyang & Yang, Xiangqun, 2006. "The compound binomial model with randomized decisions on paying dividends," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 1-18, August.
    5. Yuen, Kam C. & Wang, Guojing & Wu, Rong, 2006. "On the renewal risk process with stochastic interest," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1496-1510, October.
    6. Yuen, Kam C. & Wang, Guojing & Li, Wai K., 2007. "The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 104-112, January.
    7. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
    8. Yang, Wenquan & Hu, Yijun, 2009. "Upper bounds for ultimate ruin probabilities in the Sparre Andersen risk model with interest and a nonlinear dividend barrier," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 63-69, January.
    9. 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.
    10. Cai, Jun, 2004. "Ruin probabilities and penalty functions with stochastic rates of interest," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 53-78, July.
    11. Zan Yu & Lianzeng Zhang, 2024. "Computing the Gerber-Shiu function with interest and a constant dividend barrier by physics-informed neural networks," Papers 2401.04378, arXiv.org.
    12. Psarrakos, Georgios & Politis, Konstadinos, 2008. "Tail bounds for the joint distribution of the surplus prior to and at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 163-176, February.
    13. Dassios, Angelos & Wu, Shanle, 2008. "Parisian ruin with exponential claims," LSE Research Online Documents on Economics 32033, London School of Economics and Political Science, LSE Library.
    14. Li, Shuanming & Garrido, José, 2002. "On the time value of ruin in the discrete time risk model," DEE - Working Papers. Business Economics. WB wb021812, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    15. Cheng, Shixue & Gerber, Hans U. & Shiu, Elias S. W., 2000. "Discounted probabilities and ruin theory in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 239-250, May.
    16. He, Jingmin & Wu, Rong & Zhang, Huayue, 2009. "Total duration of negative surplus for the risk model with debit interest," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1320-1326, May.
    17. Liu, Xiangdong & Xiong, Jie & Zhang, Shuaiqi, 2015. "The Gerber–Shiu discounted penalty function in the classical risk model with impulsive dividend policy," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 183-190.
    18. Wang, Rongming & Yang, Hailiang & Wang, Hanxing, 2004. "On the distribution of surplus immediately after ruin under interest force and subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 703-714, December.
    19. Chiu, S. N. & Yin, C. C., 2003. "The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 59-66, August.
    20. Cheung, Eric C.K. & Landriault, David, 2010. "A generalized penalty function with the maximum surplus prior to ruin in a MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 127-134, February.

    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:77:y:2007:i:8:p:761-768. 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.