IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v54y2000i1p99-112.html
   My bibliography  Save this article

Computer treatment of the integro-differential equations of collective non-ruin; the finite time case

Author

Listed:
  • Makroglou, Athena

Abstract

An important problem of collective non-ruin is the estimation of the probabilities R(z,t) and R(z) of the finite and ultimate non-ruin, respectively, where t is time and z the initial reserve. The governing equations are first-order Volterra integro-differential equations, partial (PVIDEs) in the finite time case and ordinary (VIDEs) in the ultimate non-ruin case, respectively.

Suggested Citation

  • Makroglou, Athena, 2000. "Computer treatment of the integro-differential equations of collective non-ruin; the finite time case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 99-112.
  • Handle: RePEc:eee:matcom:v:54:y:2000:i:1:p:99-112
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475400002020
    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. Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
    2. Sundt, Bjorn & Teugels, Jozef L., 1997. "The adjustment function in ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 85-94, April.
    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. 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. 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.
    3. Phung Duy Quang, 2017. "Upper Bounds for Ruin Probability in a Controlled Risk Process under Rates of Interest with Homogenous Markov Chains," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(3), pages 1-4.
    4. 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.
    5. Rulliere, Didier & Loisel, Stephane, 2005. "The win-first probability under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 421-442, December.
    6. Jasiulewicz, Helena, 2001. "Probability of ruin with variable premium rate in a Markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 291-296, October.
    7. 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.
    8. Paulsen, Jostein, 1998. "Ruin theory with compounding assets -- a survey," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 3-16, May.
    9. Leveille, Ghislain & Garrido, Jose, 2001. "Moments of compound renewal sums with discounted claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 217-231, April.
    10. 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.
    11. 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.
    12. Albrecher, Hansjorg & Teugels, Jozef L. & Tichy, Robert F., 2001. "On a gamma series expansion for the time-dependent probability of collective ruin," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 345-355, December.
    13. Konstantinides, Dimitrios & Tang, Qihe & Tsitsiashvili, Gurami, 2002. "Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 447-460, December.
    14. Cai, Jun & Dickson, David C. M., 2003. "Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 61-71, February.
    15. Diasparra, Maikol & Romera, Rosario, 2006. "Optimal policies for discrete time risk processes with a Markov chain investment model," DES - Working Papers. Statistics and Econometrics. WS ws062408, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Huang, Tao & Zhao, Ruiqing & Tang, Wansheng, 2009. "Risk model with fuzzy random individual claim amount," European Journal of Operational Research, Elsevier, vol. 192(3), pages 879-890, February.
    17. 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.
    18. Kalashnikov, Vladimir & Konstantinides, Dimitrios, 2000. "Ruin under interest force and subexponential claims: a simple treatment," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 145-149, August.
    19. Sundt, Bjorn & Teugels, Jozef L., 1997. "The adjustment function in ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 85-94, April.
    20. Dickson, David C. M. & Waters, Howard R., 1999. "Ruin probabilities with compounding assets," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 49-62, September.

    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:matcom:v:54:y:2000:i:1:p:99-112. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.