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Finite time ruin problems for the Erlang(2) risk model

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  • Dickson, David C.M.
  • Li, Shuanming

Abstract

We consider the Erlang(2) risk model and derive expressions for the density of the time to ruin and the joint density of the time to ruin and the deficit at ruin when the individual claim amount distribution is (i) an exponential distribution and (ii) an Erlang(2) distribution. We also consider the special case when the initial surplus is zero.

Suggested Citation

  • Dickson, David C.M. & Li, Shuanming, 2010. "Finite time ruin problems for the Erlang(2) risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 12-18, February.
  • Handle: RePEc:eee:insuma:v:46:y:2010:i:1:p:12-18
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    References listed on IDEAS

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    1. Borovkov, Konstantin A. & Dickson, David C.M., 2008. "On the ruin time distribution for a Sparre Andersen process with exponential claim sizes," Insurance: Mathematics and Economics, Elsevier, pages 1104-1108.
    2. Willmot, Gordon E., 2007. "On the discounted penalty function in the renewal risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, pages 17-31.
    3. Dickson, David C.M., 2008. "Some Explicit Solutions for the Joint Density of the Time of Ruin and the Deficit at Ruin," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(01), pages 259-276, May.
    4. Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, pages 391-408.
    5. Garcia, Jorge M.A., 2005. "Explicit Solutions for Survival Probabilities in the Classical Risk Model," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 35(01), pages 113-130, May.
    6. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, pages 205-222.
    7. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, pages 333-344.
    8. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, pages 205-222.
    9. Dickson, David C.M. & Willmot, Gordon E., 2005. "The Density of the Time to Ruin in the Classical Poisson Risk Model," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 35(01), pages 45-60, May.
    10. Drekic, Steve & Willmot, Gordon E., 2003. "On the Density and Moments of the Time of Ruin with Exponential Claims," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 33(01), pages 11-21, May.
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    Cited by:

    1. Frostig, Esther & Pitts, Susan M. & Politis, Konstadinos, 2012. "The time to ruin and the number of claims until ruin for phase-type claims," Insurance: Mathematics and Economics, Elsevier, pages 19-25.
    2. Dickson, David C.M. & Li, Shuanming, 2013. "The distributions of the time to reach a given level and the duration of negative surplus in the Erlang(2) risk model," Insurance: Mathematics and Economics, Elsevier, pages 490-497.
    3. repec:eee:apmaco:v:315:y:2017:i:c:p:319-330 is not listed on IDEAS
    4. Feng, Runhuan & Volkmer, Hans W., 2012. "Modeling credit value adjustment with downgrade-triggered termination clause using a ruin theoretic approach," Insurance: Mathematics and Economics, Elsevier, pages 409-421.
    5. Wong, Jeff T.Y. & Cheung, Eric C.K., 2015. "On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps," Insurance: Mathematics and Economics, Elsevier, pages 280-290.

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