IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1804.05694.html
   My bibliography  Save this paper

Extremal dependence and spatial risk measures for insured losses due to extreme winds

Author

Listed:
  • Erwan Koch

Abstract

A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introduced by Koch (2017, 2019), we quantify the risk of losses due to extreme wind speeds. The insured cost due to wind events is proportional to the wind speed at a power ranging typically between 2 and 12. Hence we first perform a detailed study of the correlation structure of powers of the Brown-Resnick max-stable random fields and look at the influence of the power. Then, using the latter results, we thoroughly investigate spatial risk measures associated with variance and induced by powers of max-stable random fields. In addition, we show that spatial risk measures associated with several classical risk measures and induced by such cost fields satisfy (at least part of) the previously mentioned axioms under conditions which are generally satisfied for the risk of damaging extreme wind speeds. In particular, we specify the rates of spatial diversification in different cases, which is valuable for the insurance industry.

Suggested Citation

  • Erwan Koch, 2018. "Extremal dependence and spatial risk measures for insured losses due to extreme winds," Papers 1804.05694, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1804.05694
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1804.05694
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Philippe Naveau & Armelle Guillou & Daniel Cooley & Jean Diebolt, 2009. "Modelling pairwise dependence of maxima in space," Biometrika, Biometrika Trust, vol. 96(1), pages 1-17.
    2. Martin Schlather, 2003. "A dependence measure for multivariate and spatial extreme values: Properties and inference," Biometrika, Biometrika Trust, vol. 90(1), pages 139-156, March.
    3. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 201-212, November.
    4. R. Huser & A. C. Davison, 2013. "Composite likelihood estimation for the Brown--Resnick process," Biometrika, Biometrika Trust, vol. 100(2), pages 511-518.
    5. Padoan, S. A. & Ribatet, M. & Sisson, S. A., 2010. "Likelihood-Based Inference for Max-Stable Processes," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 263-277.
    6. Christian Yann Robert & Erwan Koch & Clément Dombry, 2018. "A central limit theorem for functions of stationary max-stable random fields on R d," Post-Print hal-02006799, HAL.
    7. Kabluchko, Zakhar & Schlather, Martin, 2010. "Ergodic properties of max-infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 281-295, March.
    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. Koch, Erwan & Robert, Christian Y., 2022. "Stochastic derivative estimation for max-stable random fields," European Journal of Operational Research, Elsevier, vol. 302(2), pages 575-588.
    2. Erwan Koch & Christian Y. Robert, 2018. "Stochastic derivative estimation for max-stable random fields," Papers 1812.05893, arXiv.org, revised Nov 2020.

    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. Erwan Koch, 2019. "Spatial Risk Measures and Rate of Spatial Diversification," Risks, MDPI, vol. 7(2), pages 1-26, May.
    2. Whitney K. Huang & Daniel S. Cooley & Imme Ebert-Uphoff & Chen Chen & Snigdhansu Chatterjee, 2019. "New Exploratory Tools for Extremal Dependence: $$\chi $$ χ Networks and Annual Extremal Networks," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 484-501, September.
    3. Wang, Yixin & So, Mike K.P., 2016. "A Bayesian hierarchical model for spatial extremes with multiple durations," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 39-56.
    4. M. Ghil & Pascal Yiou & Stéphane Hallegatte & B. D. Malamud & P. Naveau & A. Soloviev & P. Friederichs & V. Keilis-Borok & D. Kondrashov & V. Kossobokov & O. Mestre & C. Nicolis & H. W. Rust & P. Sheb, 2011. "Extreme events: dynamics, statistics and prediction," Post-Print hal-00716514, HAL.
    5. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2021. "Semiparametric estimation for space-time max-stable processes: an F-madogram-based approach," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 241-276, July.
    6. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2020. "Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 479-522, June.
    7. Raphaël Huser & Marc G. Genton, 2016. "Non-Stationary Dependence Structures for Spatial Extremes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 470-491, September.
    8. Harald Schellander & Tobias Hell, 2018. "Modeling snow depth extremes in Austria," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(3), pages 1367-1389, December.
    9. John H. J. Einmahl & Anna Kiriliouk & Andrea Krajina & Johan Segers, 2016. "An M-estimator of spatial tail dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 275-298, January.
    10. Einmahl, John & Kiriliouk, Anna & Segers, Johan, 2016. "A continuous updating weighted least squares estimator of tail dependence in high dimensions," LIDAM Discussion Papers ISBA 2016002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Padoan, Simone A., 2013. "Extreme dependence models based on event magnitude," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 1-19.
    12. Boris Beranger & Simone A. Padoan & Scott A. Sisson, 2017. "Models for Extremal Dependence Derived from Skew-symmetric Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 21-45, March.
    13. Alexis Bienvenüe & Christian Y. Robert, 2017. "Likelihood Inference for Multivariate Extreme Value Distributions Whose Spectral Vectors have known Conditional Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 130-149, March.
    14. Koch, Erwan & Dombry, Clément & Robert, Christian Y., 2019. "A central limit theorem for functions of stationary max-stable random fields on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3406-3430.
    15. Padoan, Simone A., 2011. "Multivariate extreme models based on underlying skew-t and skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 977-991, May.
    16. Koch, Erwan & Robert, Christian Y., 2022. "Stochastic derivative estimation for max-stable random fields," European Journal of Operational Research, Elsevier, vol. 302(2), pages 575-588.
    17. Samuel A. Morris & Brian J. Reich & Emeric Thibaud, 2019. "Exploration and Inference in Spatial Extremes Using Empirical Basis Functions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 555-572, December.
    18. Lee, Xing Ju & Hainy, Markus & McKeone, James P. & Drovandi, Christopher C. & Pettitt, Anthony N., 2018. "ABC model selection for spatial extremes models applied to South Australian maximum temperature data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 128-144.
    19. Vettori, Sabrina & Huser, Raphael & Segers, Johan & Genton, Marc, 2017. "Bayesian Clustering and Dimension Reduction in Multivariate Extremes," LIDAM Discussion Papers ISBA 2017017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Joshua Hewitt & Miranda J. Fix & Jennifer A. Hoeting & Daniel S. Cooley, 2019. "Improved Return Level Estimation via a Weighted Likelihood, Latent Spatial Extremes Model," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 426-443, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1804.05694. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.