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Rate of convergence of the probability of ruin in the Cramér–Lundberg model to its diffusion approximation

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  • Cohen, Asaf
  • Young, Virginia R.

Abstract

We analyze the probability of ruin for the scaled classical Cramér–Lundberg (CL) risk process and the corresponding diffusion approximation. The scaling, introduced by Iglehart (1969) to the actuarial literature, amounts to multiplying the Poisson rate λ by n, dividing the claim severity by n, and adjusting the premium rate so that net premium income remains constant.

Suggested Citation

  • Cohen, Asaf & Young, Virginia R., 2020. "Rate of convergence of the probability of ruin in the Cramér–Lundberg model to its diffusion approximation," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 333-340.
    • Handle: RePEc:eee:insuma:v:93:y:2020:i:c:p:333-340
    DOI: 10.1016/j.insmatheco.2020.06.003
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    References listed on IDEAS

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    1. Broeckx, F. & Goovaerts, M. & De Vylder, F., 1986. "Ordering of risks and ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 35-39, January.
    2. De Vylder, F. & Goovaerts, M., 1984. "Bounds for classical ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 3(2), pages 121-131, April.
    3. Gerber, Hans U. & Shiu, Elias S.W. & Smith, Nathaniel, 2008. "Methods for estimating the optimal dividend barrier and the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 243-254, February.
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    Citations

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    Cited by:

    1. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    2. Kenneth Tsz Hin Ng & Wing Fung Chong, 2023. "Optimal Investment in Defined Contribution Pension Schemes with Forward Utility Preferences," Papers 2303.08462, arXiv.org, revised Sep 2023.
    3. Marc Abeille & Bruno Bouchard & Lorenzo Croissant, 2023. "Diffusive Limit Approximation of Pure-Jump Optimal Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 147-176, January.

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    More about this item

    Keywords

    Investment analysis; Probability of ruin; Cramér–Lundberg risk process; Diffusion approximation; Approximation error;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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