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Sensitivity Analysis of Insurance Risk Models via Simulation

Author

Listed:
  • Søren Asmussen

    (Department of Mathematical Statistics, University of Lund, Box 118, 221 00 Lund, Sweden)

  • Reuven Y. Rubinstein

    (William Davidson Faculty of Industrial Engineering and Management, Technion, Haifa, Israel)

Abstract

We show how, from a single simulation run, to estimate the ruin probabilities and their sensitivities (derivatives) in a classic insurance risk model under various distributions of the number of claims and the claim size. Similar analysis is given for the tail probabilities of the accumulated claims during a fixed period. We perform sensitivity analysis with respect to both distributional and structural parameters of the underlying risk model. In the former case, we use the score function method and in the latter, a combination of the push-out method and the score function. We finally show how, from the same sample path, to derive a consistent estimator of the optimal solution in an optimization problem associated with excess-of-loss reinsurance.

Suggested Citation

  • Søren Asmussen & Reuven Y. Rubinstein, 1999. "Sensitivity Analysis of Insurance Risk Models via Simulation," Management Science, INFORMS, vol. 45(8), pages 1125-1141, August.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:8:p:1125-1141
    DOI: 10.1287/mnsc.45.8.1125
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    References listed on IDEAS

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    1. Kriman, V. & Rubinstein, R.Y., 1995. "Polynomial Time Algorithms for Estimation of Rare Events in Queueing Models," Other publications TiSEM bb044e22-c7f1-41f2-b4d9-2, Tilburg University, School of Economics and Management.
    2. Peter W. Glynn & Donald L. Iglehart, 1989. "Importance Sampling for Stochastic Simulations," Management Science, INFORMS, vol. 35(11), pages 1367-1392, November.
    3. Philip Heidelberger & Don Towsley, 1989. "Sensitivity Analysis from Sample Paths Using Likelihoods," Management Science, INFORMS, vol. 35(12), pages 1475-1488, December.
    4. Asmussen, S. & Binswanger, K., 1997. "Simulation of Ruin Probabilities for Subexponential Claims," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 297-318, November.
    5. Kriman, V. & Rubinstein, R.Y., 1995. "Polynomial Time Algorithms for Estimation of Rare Events in Queueing Models," Discussion Paper 1995-12, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Ankush Agarwal & Stefano de Marco & Emmanuel Gobet & Gang Liu, 2017. "Rare event simulation related to financial risks: efficient estimation and sensitivity analysis," Working Papers hal-01219616, HAL.
    2. Shengkun Xie, 2021. "Improving Explainability of Major Risk Factors in Artificial Neural Networks for Auto Insurance Rate Regulation," Risks, MDPI, vol. 9(7), pages 1-21, July.
    3. Riccardo Gatto, 2018. "The Stability of the Aggregate Loss Distribution," Risks, MDPI, vol. 6(3), pages 1-13, September.

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