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A note on some joint distribution functions involving the time of ruin

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  • Dickson, David C.M.

Abstract

In a recent paper, Willmot (2015) derived an expression for the joint distribution function of the time of ruin and the deficit at ruin in the classical risk model. We show how his approach can be applied to obtain a simpler expression, and by interpreting this expression by probabilistic reasoning we obtain solutions for more general risk models. We also discuss how some of Willmot’s results relate to existing literature on the probability and severity of ruin.

Suggested Citation

  • Dickson, David C.M., 2016. "A note on some joint distribution functions involving the time of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 120-124.
    • Handle: RePEc:eee:insuma:v:67:y:2016:i:c:p:120-124
    DOI: 10.1016/j.insmatheco.2015.12.005
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    References listed on IDEAS

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    1. Jiandong Ren, 2008. "On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 198-206.
    2. Willmot, Gordon E., 2007. "On the discounted penalty function in the renewal risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 17-31, July.
    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, Cambridge University Press, vol. 38(1), pages 259-276, May.
    4. Li, Jingchao & Dickson, David C.M. & Li, Shuanming, 2015. "Some ruin problems for the MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 1-8.
    5. Dickson, D. C. M., 2007. "Some Finite Time Ruin Problems," Annals of Actuarial Science, Cambridge University Press, vol. 2(2), pages 217-232, September.
    6. Gerber, Hans U. & Goovaerts, Marc J. & Kaas, Rob, 1987. "On the Probability and Severity of Ruin," ASTIN Bulletin, Cambridge University Press, vol. 17(2), pages 151-163, November.
    7. Garcia, Jorge M.A., 2005. "Explicit Solutions for Survival Probabilities in the Classical Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 113-130, May.
    8. Dickson, David C. M. & Waters, Howard R., 1992. "The Probability and Severity of Ruin in Finite and Infinite Time," ASTIN Bulletin, Cambridge University Press, vol. 22(2), pages 177-190, November.
    9. Dickson, David C.M. & Willmot, Gordon E., 2005. "The Density of the Time to Ruin in the Classical Poisson Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 45-60, May.
    Full references (including those not matched with items on IDEAS)

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