Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-24T03:40:12.972Z Has data issue: false hasContentIssue false
  • English
  • Français

ON MARINE LIABILITY PORTFOLIO MODELING

Published online by Cambridge University Press:  13 December 2019

William Guevara-Alarcón Open the ORCID record for William Guevara-Alarcón [Opens in a new window] ,
Hansjörg Albrecher Open the ORCID record for Hansjörg Albrecher [Opens in a new window]  and
Parvez Chowdhury
William Guevara-Alarcón*
Affiliation:
SCOR Switzerland Ltd, General Guisan Quai 26, 8002 Zürich, Switzerland Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, 1015 Lausanne, Switzerland, E-Mail: wguevara@scor.com, wmguevaraa@unal.edu.co
Hansjörg Albrecher
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, 1015 Lausanne, Switzerland Swiss Finance Institute, Lausanne, Switzerland, E-Mail: hansjoerg.albrecher@unil.ch
Parvez Chowdhury
Affiliation:
SCOR Switzerland Ltd, General Guisan Quai 26, 8002 Zürich, Switzerland, E-Mail: pchowdhury@scor.com
*
E-Mail: wguevara@scor.com, wmguevaraa@unal.edu.co
Get access Rights & Permissions [Opens in a new window]

Abstract

Marine is the oldest type of insurance coverage. Nevertheless, unlike cargo and hull covers, marine liability is a rather young line of business with claims that can have very heavy and long tails. For reinsurers, the accumulation of losses from an event insured by various Protection and Indemnity clubs is an additional source for very large claims in the portfolio. In this paper, we first describe some recent developments of the marine liability market and then statistically analyze a data set of large losses for this line of business in a detailed manner both in terms of frequency and severity, including censoring techniques and tests for stationarity over time. We further formalize and examine an optimization problem that occurs for reinsurers participating in XL on XL coverages in this line of business and give illustrations of its solution.

Keywords

Marine insuranceextreme value theoryPareto distributionoptimal reinsurance
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 1 , January 2020 , pp. 61 - 93
Copyright
© Astin Bulletin 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agcs (2019) Safety and Shipping Review 2019. An annual review of trends and developments in shipping losses and safety. Allianz Global Corporate & Specialty (AGCS).Google Scholar
Albrecher, H., Beirlant, J. and Teugels, J.L. (2017) Reinsurance: Actuarial and Statistical Aspects. Wiley Series in Probability and Statistics, Chichester, UK: John Wiley & Sons Ltd.Google Scholar
Albrecher, H., Bladt, M., Kortschak, D., Prettenthaler, F. and Swierczynski, T. (2019) Flood occurrence change-point analysis in the paleoflood record from Lake Mondsee (NE Alps). Global and Planetary Change, 178, 65–76.CrossRefGoogle Scholar
Beirlant, J. and Goegebeur, Y. (2003) Regression with response distributions of Pareto-type. Computational Statistics & Data Analysis, 42(4), 595–619.CrossRefGoogle Scholar
Cowling, A. and Hall, P. (1996) On pseudodata methods for removing boundary effects in kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological), 58(3), 551–563.CrossRefGoogle Scholar
Dantzig, G.B. (1951) Maximization of a linear function of variables subject to linear inequalities, chapter. In Activity Analysis of Production and Allocation, pp. 339–347. New York: John Wiley & Sons Ltd.Google Scholar
Dekkers, A.L.M., Einmahl, J.H.J. and de Hann, L. (1989) A moment estimator for the index of an extreme-value distribution. Annals of Statistics, 17(4), 1833–1855.CrossRefGoogle Scholar
Diggle, P. (1985) A kernel method for smoothing point process data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 34(2), 138–147.Google Scholar
Einmahl, J., Fils-Villetard, A. and Guillou, A. (2008) Statistics of extremes under random censoring. Bernoulli, 14(1), 207–227.CrossRefGoogle Scholar
Einmahl, J.H.J., de Haan, L. and Zhou, C. (2016) Statistics of heteroscedastic extremes. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 78(1), 31–51.CrossRefGoogle Scholar
Farr, D., Subasinghe, H., Newman, A., Gingell, C., Stuart, D., Montague, E., Peacock, E., Dawson, G., Rama, G., Gardner, J., Patel, K., Frontado, L., Lo, M., Haria, S., Ashraf, S., Hodkinson, S. and Hartington, T. (2014) Marine and energy pricing. GIRO Conference.Google Scholar
Futterknecht, O., Pain, D. and Turner, G. (2013) Navigating recent developments in marine and airline insurance. Sigma. Swiss Re (4).Google Scholar
Giro (2011) Risk appetite for a general insurance undertaking. Risk Appetite Working Party (GIRO).Google Scholar
Hall, P. (1982) On some simple estimates of an exponent of regular variation. Journal of the Royal Statistical Society. Series B (Methodological), 44(1), 37–42.CrossRefGoogle Scholar
Hill, B.M. (1975) A simple general approach to inference about the tail of a distribution. Annals of Statistics, 3(5), 1163–1173.CrossRefGoogle Scholar
Holland, D.M. (2009) A brief history of reinsurance. Reinsurance News, Special Edition, 65, 4–29.Google Scholar
Homer, D. and Li, M. (2017) Notes on Using Property Catastrophe Model Results. Casualty Actuarial Society E-Forum 2.Google Scholar
Igp&I (2015) Annual Review 2014/2015. International Group of P&I Clubs (IGP&I).Google Scholar
Igp&I (2017) Annual Review 2016/2017. International Group of P&I Clubs (IGP&I).Google Scholar
Itopf (2019) Oil Tanker Spill Statistics 2018. The International Tanker Owners Pollution Federation Limited (ITOPF).Google Scholar
Kaas, R., Goovaerts, M., Dhaene, J. and Denuit, M. (2008) Modern Actuarial Risk Theory. Using R, Second Edition. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Lloyds (2013) The Challenges and Implications of Removing Shipwrecks in the 21st Century. London, UK: Lloyd’s.Google Scholar
Luenberger, D.G. and Ye, Y. (2008) Linear and Nonlinear Programming, Third Edition. International Series in Operations Research & Management Science. New York: Springer.CrossRefGoogle Scholar
McNeil, A.J. (1997) Estimating the tails of loss severity distributions using extreme value theory. Astin Bulletin, 27(1), 117–137.CrossRefGoogle Scholar
Merz, B., Nguyen, V.D. and Vorogushyn, S. (2016) Temporal clustering of floods in germany: Do flood-rich and flood-poor periods exist? Journal of Hydrology, 541(B), 824–838.CrossRefGoogle Scholar
Mitchell-Wallace, K., Jones, M., Hillier, J. and Foote, M. (2017) Natural Catastrophe Risk Management and Modelling. A Practitioner’s Guide. Chichester: John Wiley & Sons Ltd.Google Scholar
Seltmann, A. (2019) Global marine insurance report 2019. International Union of Marine Insurance (IUMI) Conference.Google Scholar
Sheather, S.J. and Jones, M.C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 53(3), 683–690.Google Scholar
Swiss Re (2003) Marine Insurance. Swiss Re.Google Scholar
Vanderbei, R.J. (2014) Linear Programming. Foundations and Extensions. Fourth Edition. International Series in Operations Research & Management Science. New York: Springer,.Google Scholar
White, I.C. and Molloy, F.C. (2003) Factors that determine the cost of oil spills. International Oil Spill Conference Proceedings, Vol. 1, pp. 1225–1229.CrossRefGoogle Scholar