IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i16p2692-2699.html
   My bibliography  Save this article

On the time to ruin and the deficit at ruin in a risk model with double-sided jumps

Author

Listed:
  • Xing, Xiaoyu
  • Zhang, Wei
  • Jiang, Yiming

Abstract

In this paper, we consider a jump diffusion risk model, which consists of a Brownian motion, phase type distributed positive claims and general negative claims. The distributions of the time to ruin and the deficit at ruin will be studied by using Rouché's Theorem, martingale and matrix analysis. We derive an explicit joint Laplace transform for the time to ruin and the deficit at ruin, as well as the Laplace transform for the time to ruin. Furthermore, our results still hold even when positive claims are rationally distributed.

Suggested Citation

  • Xing, Xiaoyu & Zhang, Wei & Jiang, Yiming, 2008. "On the time to ruin and the deficit at ruin in a risk model with double-sided jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2692-2699, November.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2692-2699
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00186-7
    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. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    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. Zhang, Zhimin & Yang, Hu, 2010. "A generalized penalty function in the Sparre-Andersen risk model with two-sided jumps," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 597-607, April.
    2. Chuancun Yin & Yuzhen Wen & Zhaojun Zong & Ying Shen, 2013. "The first passage time problem for mixed-exponential jump processes with applications in insurance and finance," Papers 1302.6762, arXiv.org, revised Jun 2014.
    3. 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.

    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. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078.
    2. Boyarchenko Svetlana & Levendorskii Sergei Z, 2006. "General Option Exercise Rules, with Applications to Embedded Options and Monopolistic Expansion," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-53, June.
    3. Tung-Lung Wu, 2020. "Boundary Crossing Probabilities of Jump Diffusion Processes to Time-Dependent Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 13-24, March.
    4. Doney, Ron & Maller, Ross & Savov, Mladen, 2009. "Renewal theorems and stability for the reflected process," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1270-1297, April.
    5. Kimura, Toshikazu, 2008. "Valuing finite-lived Russian options," European Journal of Operational Research, Elsevier, vol. 189(2), pages 363-374, September.
    6. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    7. 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.
    8. Kazutoshi Yamazaki, 2017. "Inventory Control for Spectrally Positive Lévy Demand Processes," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 212-237, January.
    9. Zbigniew Palmowski & Jos'e Luis P'erez & Kazutoshi Yamazaki, 2020. "Double continuation regions for American options under Poisson exercise opportunities," Papers 2004.03330, arXiv.org.
    10. Kuznetsov, A. & Peng, X., 2012. "On the Wiener–Hopf factorization for Lévy processes with bounded positive jumps," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2610-2638.
    11. Chi, Yichun, 2010. "Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 385-396, April.
    12. Zhimin Zhang & Hailiang Yang & Hu Yang, 2012. "On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 973-995, December.
    13. Michael C. Fu & Bingqing Li & Guozhen Li & Rongwen Wu, 2017. "Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions," Management Science, INFORMS, vol. 63(11), pages 3961-3977, November.
    14. Irmina Czarna & Zbigniew Palmowski, 2014. "Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 239-256, April.
    15. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
    16. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    17. Kim, Jerim & Kim, Jeongsim & Joo Yoo, Hyun & Kim, Bara, 2015. "Pricing external barrier options in a regime-switching model," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 123-143.
    18. Baurdoux, E.J. & Palmowski, Z. & Pistorius, M.R., 2017. "On future drawdowns of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2679-2698.
    19. Benjamin Avanzi & Jos'e-Luis P'erez & Bernard Wong & Kazutoshi Yamazaki, 2016. "On optimal joint reflective and refractive dividend strategies in spectrally positive L\'evy models," Papers 1607.01902, arXiv.org, revised Nov 2016.
    20. Ning Cai & Wei Zhang, 2020. "Regime Classification and Stock Loan Valuation," Operations Research, INFORMS, vol. 68(4), pages 965-983, July.

    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:78:y:2008:i:16:p:2692-2699. 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.