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Recursive Methods for Computing Finite-Time Ruin Probabilities for Phase-Distributed Claim Sizes

Author

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  • Stanford, D.A.
  • StroiÅ„ski, K.J.

Abstract

Finite time ruin methods typically rely on diffusion approximations or discretization. We propose a new method by looking at the surplus process embedded at claim instants and develop a recursive scheme for calculating ruin probabilities. It is assumed that claim sizes follow a phase-type distribution. The proposed method is exact. The application of the method reveals where in the future the relative vulnerability to the company lies.

Suggested Citation

  • Stanford, D.A. & StroiÅ„ski, K.J., 1994. "Recursive Methods for Computing Finite-Time Ruin Probabilities for Phase-Distributed Claim Sizes," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 235-254, November.
    • Handle: RePEc:cup:astinb:v:24:y:1994:i:02:p:235-254_00
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    Cited by:

    1. Dickson, David C.M., 2012. "The joint distribution of the time to ruin and the number of claims until ruin in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 334-337.
    2. Yi Lu, 2016. "On the Evaluation of Expected Penalties at Claim Instants That Cause Ruin in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 237-255, March.
    3. Landriault, David & Shi, Tianxiang & Willmot, Gordon E., 2011. "Joint densities involving the time to ruin in the Sparre Andersen risk model under exponential assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 371-379.
    4. Egidio dos Reis, Alfredo D., 2002. "How many claims does it take to get ruined and recovered?," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 235-248, October.

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