IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v62y2003i3p277-287.html
   My bibliography  Save this article

Simulation methods in ruin models with non-linear dividend barriers

Author

Listed:
  • Albrecher, Hansjörg
  • Kainhofer, Reinhold
  • Tichy, Robert F.

Abstract

In this paper, a collective risk reserve process of an insurance portfolio characterized by a homogeneous Poisson claim number process, a constant premium flow and independent and identically distributed claims is considered. In the presence of a non-linear dividend barrier strategy and interest on the free reserve we derive equations for the probability of ruin and the expected present value of dividend payments which give rise to several numerical number-theoretic solution techniques. For various claim size distributions and a parabolic barrier numerical tests and comparisons of these techniques are performed. In particular, the efficiency gain obtained by implementing low-discrepancy sequences instead of pseudo-random sequences is investigated.

Suggested Citation

  • Albrecher, Hansjörg & Kainhofer, Reinhold & Tichy, Robert F., 2003. "Simulation methods in ruin models with non-linear dividend barriers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 277-287.
    • Handle: RePEc:eee:matcom:v:62:y:2003:i:3:p:277-287
    DOI: 10.1016/S0378-4754(02)00225-2
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475402002252
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/S0378-4754(02)00225-2?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. Paulsen, Jostein & Gjessing, Hakon K., 1997. "Optimal choice of dividend barriers for a risk process with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 215-223, October.
    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. Jin, Can & Li, Shuanming & Wu, Xueyuan, 2016. "On the occupation times in a delayed Sparre Andersen risk model with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 304-316.
    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. Hubalek, Friedrich & Schachermayer, Walter, 2004. "Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 193-225, April.
    4. Chi, Yichun & Jaimungal, Sebastian & Lin, X. Sheldon, 2010. "An insurance risk model with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 52-66, February.

    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. 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.
    2. Bo, Lijun & Song, Renming & Tang, Dan & Wang, Yongjin & Yang, Xuewei, 2012. "Lévy risk model with two-sided jumps and a barrier dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 280-291.
    3. M. Mercedes Claramunt Bielsa & Maite Teresa Marmol Jimenez & Antonio Alegre Escolano, 2002. "Discrete analysis of dividend payments in a non-life insurance portfolio," Working Papers in Economics 85, Universitat de Barcelona. Espai de Recerca en Economia.
    4. 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.
    5. Runhuan Feng & Hans Volkmer & Shuaiqi Zhang & Chao Zhu, 2011. "Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model," Papers 1106.2781, arXiv.org, revised Nov 2014.
    6. Pelsser, Antoon A.J. & Laeven, Roger J.A., 2013. "Optimal dividends and ALM under unhedgeable risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 515-523.
    7. He, Lin & Liang, Zongxia, 2008. "Optimal financing and dividend control of the insurance company with proportional reinsurance policy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 976-983, June.
    8. Albrecher, Hansjörg & Thonhauser, Stefan, 2008. "Optimal dividend strategies for a risk process under force of interest," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 134-149, August.
    9. 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.
    10. Dassios, Angelos & Wu, Shanle, 2009. "On barrier strategy dividends with Parisian implementation delay for classical surplus processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 195-202, October.
    11. Bjarne Højgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327.
    12. Irgens, Christian & Paulsen, Jostein, 2004. "Optimal control of risk exposure, reinsurance and investments for insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 21-51, August.
    13. Leung, Kwai Sun & Kwok, Yue Kuen & Leung, Seng Yuen, 2008. "Finite-time dividend-ruin models," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 154-162, February.
    14. Dassios, Angelos & Wu, Shanle, 2011. "Barrier strategies with Parisian delay," LSE Research Online Documents on Economics 32024, London School of Economics and Political Science, LSE Library.
    15. 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.
    16. 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.
    17. Yao, Kai & Qin, Zhongfeng, 2015. "A modified insurance risk process with uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 227-233.
    18. Chuancun Yin & Yuzhen Wen, 2013. "An extension of Paulsen-Gjessing's risk model with stochastic return on investments," Papers 1302.6757, arXiv.org.
    19. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    20. 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.

    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:62:y:2003:i:3:p:277-287. 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.