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Gamma Processes and Finite Time Survival Probabilities

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  • Dickson, David C. M.
  • Waters, Howard R.

Abstract

In this paper we derive formulae for finite time survival probabilities when the aggregate claims process is a Gamma process. We illustrate how a compound Poisson process can be approximated by a Gamma process and by a process defined as a translated Gamma process. We also show how survival probabilities for a compound Poisson process can be approximated by those for a Gamma process or a translated Gamma process.

Suggested Citation

  • Dickson, David C. M. & Waters, Howard R., 1993. "Gamma Processes and Finite Time Survival Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 259-272, November.
    • Handle: RePEc:cup:astinb:v:23:y:1993:i:02:p:259-272_01
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    Cited by:

    1. George Bouzianis & Lane P. Hughston, 2019. "Determination Of The Lévy Exponent In Asset Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-18, February.
    2. Hao, Xuemiao & Li, Xuan & Shimizu, Yasutaka, 2013. "Finite-time survival probability and credit default swaps pricing under geometric Lévy markets," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 14-23.
    3. Zhang, Dewei & Wang, Yiqi & Wang, Jingjing & Xu, Weidong, 2013. "Liquidity management of foreign exchange reserves in continuous time," Economic Modelling, Elsevier, vol. 31(C), pages 138-142.
    4. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
    5. Başak Bulut Karageyik & Şule Şahin, 2017. "Determination of the Optimal Retention Level Based on Different Measures," JRFM, MDPI, vol. 10(1), pages 1-21, January.
    6. Michna, Zbigniew, 2011. "Formula for the supremum distribution of a spectrally positive [alpha]-stable Lévy process," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 231-235, February.
    7. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.

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