IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws093513.html
   My bibliography  Save this paper

Inequalities for the ruin probability in a controlled discrete-time risk process

Author

Listed:
  • Diasparra, Maikol
  • Romera, Rosario

Abstract

Ruin probabilities in a controlled discrete-time risk process with a Markov chain interest are studied. To reduce the risk there is a possibility to reinsure a part or the whole reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a constant stationary policy. The relationships between these inequalities are discussed. To illustrate these results some numerical examples are included.

Suggested Citation

  • Diasparra, Maikol & Romera, Rosario, 2009. "Inequalities for the ruin probability in a controlled discrete-time risk process," DES - Working Papers. Statistics and Econometrics. WS ws093513, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws093513
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/09eeff46-9bfc-4069-8c22-4c2b00fa0ef8/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
    2. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, 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. 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.

    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. Diasparra, M. & Romera, R., 2010. "Inequalities for the ruin probability in a controlled discrete-time risk process," European Journal of Operational Research, Elsevier, vol. 204(3), pages 496-504, August.
    2. 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.
    3. Franck Adékambi & Essodina Takouda, 2020. "Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence," Risks, MDPI, vol. 8(1), pages 1-25, March.
    4. Dhiti Osatakul & Xueyuan Wu, 2021. "Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment," Risks, MDPI, vol. 9(1), pages 1-23, January.
    5. Søren Asmussen & Pierre Fiorini & Lester Lipsky & Tomasz Rolski & Robert Sheahan, 2008. "Asymptotic Behavior of Total Times for Jobs That Must Start Over if a Failure Occurs," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 932-944, November.
    6. Sanguesa, C., 2006. "Approximations of ruin probabilities in mixed Poisson models with lattice claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 69-80, August.
    7. 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.
    8. 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.
    9. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
    10. Lee, Wing Yan & Willmot, Gordon E., 2014. "On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 1-10.
    11. Psarrakos, Georgios, 2010. "On the DFR property of the compound geometric distribution with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 428-433, December.
    12. 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.
    13. El Attar Abderrahim & El Hachloufi Mostafa & Guennoun Zine El Abidine, 2017. "An Inclusive Criterion For An Optimal Choice Of Reinsurance," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 1-22, December.
    14. Baumgartner, Carolin & Gruber, Lutz F. & Czado, Claudia, 2015. "Bayesian total loss estimation using shared random effects," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 194-201.
    15. Chadjiconstantinidis, Stathis & Politis, Konstadinos, 2007. "Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 41-52, July.
    16. Kim, So-Yeun & Willmot, Gordon E., 2016. "On the analysis of ruin-related quantities in the delayed renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 77-85.
    17. Wei, Xiao & Hu, Yijun, 2008. "Ruin probabilities for discrete time risk models with stochastic rates of interest," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 707-715, April.
    18. Franco Pellerey & Cristina Zucca, 2005. "Stochastic Bounds for the Sparre Andersen Process," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 225-247, June.
    19. Willmot, Gordon E., 2002. "Compound geometric residual lifetime distributions and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 421-438, June.
    20. Woo, Jae-Kyung, 2011. "Refinements of two-sided bounds for renewal equations," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 189-196, March.

    More about this item

    Keywords

    Risk process;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cte:wsrepe:ws093513. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.