IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v45y1999i8p1125-1141.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.45.8.1125
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.45.8.1125?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Philip Heidelberger & Don Towsley, 1989. "Sensitivity Analysis from Sample Paths Using Likelihoods," Management Science, INFORMS, vol. 35(12), pages 1475-1488, December.
    2. 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.
    3. Peter W. Glynn & Donald L. Iglehart, 1989. "Importance Sampling for Stochastic Simulations," Management Science, INFORMS, vol. 35(11), pages 1367-1392, November.
    4. 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.
    5. Asmussen, S. & Binswanger, K., 1997. "Simulation of Ruin Probabilities for Subexponential Claims," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 297-318, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 55-65.
    2. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," LSE Research Online Documents on Economics 64051, London School of Economics and Political Science, LSE Library.
    3. Nam Kyoo Boots & Perwez Shahabuddin, 2001. "Simulating Tail Probabilities in GI/GI.1 Queues and Insurance Risk Processes with Subexponentail Distributions," Tinbergen Institute Discussion Papers 01-012/4, Tinbergen Institute.
    4. Philippe Jehiel & Jakub Steiner, 2020. "Selective Sampling with Information-Storage Constraints [On interim rationality, belief formation and learning in decision problems with bounded memory]," The Economic Journal, Royal Economic Society, vol. 130(630), pages 1753-1781.
    5. Albrecher Hansjörg & Kantor Josef, 2002. "Simulation of ruin probabilities for risk processes of Markovian type," Monte Carlo Methods and Applications, De Gruyter, vol. 8(2), pages 111-128, December.
    6. Prusty, B Rajanarayan & Jena, Debashisha, 2017. "A critical review on probabilistic load flow studies in uncertainty constrained power systems with photovoltaic generation and a new approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 1286-1302.
    7. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    8. Sandeep Juneja & Perwez Shahabuddin, 2001. "Fast Simulation of Markov Chains with Small Transition Probabilities," Management Science, INFORMS, vol. 47(4), pages 547-562, April.
    9. Luis Rincón & David J. Santana, 2022. "Ruin Probability for Finite Erlang Mixture Claims Via Recurrence Sequences," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2213-2236, September.
    10. Kaynar, Bahar & Ridder, Ad, 2010. "The cross-entropy method with patching for rare-event simulation of large Markov chains," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1380-1397, December.
    11. Yuguang Fan & Philip S. Griffin & Ross Maller & Alexander Szimayer & Tiandong Wang, 2017. "The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation," Risks, MDPI, vol. 5(1), pages 1-27, January.
    12. Tito Homem-de-Mello, 2007. "A Study on the Cross-Entropy Method for Rare-Event Probability Estimation," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 381-394, August.
    13. N-H Shih, 2005. "Estimating completion-time distribution in stochastic activity networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 744-749, June.
    14. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L., 2006. "Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 320-348.
    15. T. P. I. Ahamed & V. S. Borkar & S. Juneja, 2006. "Adaptive Importance Sampling Technique for Markov Chains Using Stochastic Approximation," Operations Research, INFORMS, vol. 54(3), pages 489-504, June.
    16. Martire, Antonio Luciano, 2022. "Volterra integral equations: An approach based on Lipschitz-continuity," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    17. Basrak, Bojan & Conroy, Michael & Olvera-Cravioto, Mariana & Palmowski, Zbigniew, 2022. "Importance sampling for maxima on trees," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 139-179.
    18. Francesco Strino & Fabio Parisi & Yuval Kluger, 2011. "VDA, a Method of Choosing a Better Algorithm with Fewer Validations," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-8, October.
    19. Xie, Junfei & Wan, Yan & Mills, Kevin & Filliben, James J. & Lei, Yu & Lin, Zongli, 2019. "M-PCM-OFFD: An effective output statistics estimation method for systems of high dimensional uncertainties subject to low-order parameter interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 93-118.
    20. Zdravko I. Botev & Robert Salomone & Daniel Mackinlay, 2019. "Fast and accurate computation of the distribution of sums of dependent log-normals," Annals of Operations Research, Springer, vol. 280(1), pages 19-46, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:45:y:1999:i:8:p:1125-1141. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.