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Pavla Jindrová
Viera Pacáková

Authors and WSEAS

Pavla Jindrová
Viera Pacáková

WSEAS Transactions on Business and Economics

Print ISSN: 1109-9526
E-ISSN: 2224-2899

Volume 16, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 16, 2019

Natural Catastrophe Models for Insurance Risk Management

AUTHORS: Pavla Jindrová, Viera Pacáková

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ABSTRACT: Catastrophic events are characterized by three main points: there are relatively rareness, there are statistical unexpected and there have huge impact on the whole society. Insurance or reinsurance is one way of reducing the economic consequences of catastrophic events. Risk management of insurance and reinsurance companies have to have available relevant information for estimation and adjusting premium to cover these risks. The aim of this article is to present two of the useful methods – block maxima method and peaks over threshold method. These methods use information from historical data about insured losses of natural catastrophes and estimates future insured losses. These estimates are very important for actuaries and for risk managers as one of the bases for calculating and adjusting premiums of products covering these types of risks

KEYWORDS: - Block maxima model, catastrophic events, insured losses, modelling, peaks over threshold, risk.


[1] The international Disaster Database, 2018.

[Online]. Available: https://www.emdat.be/classification

[2] Sigma No 1/2018: Natural catastrophes and man-made disasters in 2017: a year of recordbreaking losses. Swiss Re

[Online]. Available: http://institute.swissre.com/research/overview/s igma/1_2018.html

[3] Sigma 2/2017: Natural catastrophes and manmade disasters in 2016: a year of widespread damages. Swiss Re

[Online]. Available: http://institute.swissre.com/research/overview/s igma/2_2017.html

[4] Sigma No 1/2016: Natural catastrophes and man-made disasters in 2015. Swiss Re

[Online]. Available: http://institute.swissre.com/research/overview/s igma/1_2016.html

[5] Sigma No 2/2015: Natural catastrophes and man-made disasters in 2014, Swiss Re

[Online]. Available: http://media.swissre.com/documents/sigma2_2 015_en_final.pdf

[6] V. Pacáková, J. Gogola, Pareto Distribution in Insurance and Reinsurance. Conference proceedings from 9th international scientific conference Financial Management of Firms and Financial Institutions, VŠB Ostrava, 2013, pp. 298-306.

[7] P. Jindrová, Ľ. Sipková, Statistical Tools for Modeling Claim Severity. Conference proceeding from 11th International Scientific Conference on European Financial Systems 2014. Lednice, Masaryk University Brno, Czech Republic, 2014, pp. 288-294.

[8] W.G. Gilchrist, Statistical modelling with quantile functions. London: Chapman & Hall, 2000.

[9] H. A. David, H. N. Nagaraja, Order Statistics, 3rd ed. USA: John Wiley & Sons, 2003.

[10] A. J. McNeil, Estimating the Tails of Loss Severity Distributions using Extreme Value Theory. ETH Zentrum, Zürich (1996)

[Online]. Available on: https://www.casact.org/library/astin/vol27no1/1 17.pdf

[11] A. McNeil, Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory. ASTIN Bulletin, 27(1), 1997, pp. 117- 138.

[12] P. Embrechs, C. Kluppelberg, T. Mikosch, Modelling Extremal Events for Insurance and Finance. Springer, Berlin, 1997.

[13] A. Brdar Turk, A Quantitative Operational Risk Management Model, Transactions on Business and Economics, Issue 5, Volume 6, 2009, pp. 241-253.

[14] P. Jindrová, V. Pacáková, Probability Models of Natural Catastrophe Losses. In Proceedings of the 4th International Conference on Mathematical, Computational and Statistical Sciences (MCSS’16), Barcelona, 2016, pp.

[15] P. Jindrová, V. Pacáková, Modelling of extreme losses in natural disasters. International Journal of mathematical models and methods in applies sciences, Volume 10, 2016, pp. 171-178.

[16] P. Jindrová, V. Pacáková, I. Laštovičková, Modelling of Insured Losses of Natural Catastrophes Using Block Maxima Model, In Proceeding of the 3rd International Conference Applied Mathematics, Computational Science and Systems Engineering (AMCSE 2018), Roma, 2018, submitted for publication.

[17] P. Jindrová, M. Papoušková, Modelling insured catastrophe losses. Proceedings of the 10th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Zakopane, 2016, pp. 53-61.

[18] P. Jindrová, R. Jakubínský, Significance and possibilities of major accident insurance. E & M EKONOMIE A MANAGEMENT, 18, Issue 4, 2015, pp. 121-131.

[19] V. Pacáková, L. Kubec, Modelling of catastrophic losses. Scientific Papers of the University of Pardubice, Series D, Vol. XIX, No. 25, 2012, pp. 125-134.

[20] V. Pacáková, P. Jindrová, T. Musil, Quantification of risks of natural catastrophes. 8th International Scientific Conference on Managing and Modelling of Financial Risks, Ostrava, 2016, pp. 735-742.

[21] A. Davison, R. Smith, Models for exceedances over high thresholds, Journal of the Royal Statistical Society, Series B, No. 52, 1990.

[22] V. Skřivánková, A. Tartaľová, Catastrophic Risk Management in Non-life Insurance. In E&M Economics and Management, No 2, 2008, pp. 65-72.

[23] H. Zhongxian, Actuarial modelling of extremal events using transformed generalized extreme value distributions and generalized Pareto distributions, Doctoral thesis, The Ohio State University (2003)

[Online]. Available: http://www.math.ohiostate.edu/history/phds/abstracts/pdf/Han.Zhong xian.pdf.

[24] V. Pacáková, D. Brebera, Loss Distributions and Simulations in General Insurance and Reinsurance. International Journal of Mathematics and Computers in Simulation. NAUN, Volume 9, 2015, pp. 159-168.

[25] R. Fisher, L. Tippett, Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proceedings of the Cambridge Philosophical Society, 24, 1928, pp. 180-190.

[26] A. Balkema, L. de Haan, Residual life time at great age, Annals of Probability, 2, 1974.

[27] J. Pickands, Statistical inference using extreme order statistics, The Annals of Statistics, 3, 1975, pp. 119-131.

WSEAS Transactions on Business and Economics, ISSN / E-ISSN: 1109-9526 / 2224-2899, Volume 16, 2019, Art. #2, pp. 9-17

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