Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-qcsxw Total loading time: 0.236 Render date: 2022-08-18T04:38:07.131Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

A COPULA REGRESSION FOR MODELING MULTIVARIATE LOSS TRIANGLES AND QUANTIFYING RESERVING VARIABILITY

Published online by Cambridge University Press:  08 October 2013

Peng Shi*
Affiliation:
Actuarial Science, Risk Management, and Insurance Department, Wisconsin School of Business, University of Wisconsin–Madison, 975 University Avenue, Madison, Wisconsin 53706, USA E-Mail: pshi@bus.wisc.edu

Abstract

This article proposes a claims reserving model for dependent lines of business with the accommodation of association among triangles by a copula function. We show that the family of elliptical copulas is a pretty convenient choice to capture the dependencies introduced by various sources, including the common calendar year effects. To quantify the associated reserving variability, we resort to parametric bootstrapping techniques for simulating the predictive distribution of outstanding liabilities and for calculating the three components of predictive uncertainty: the model error, the process error and the estimation error. Numerical analysis is performed for a portfolio of casualty insurance from a major U.S. insurer.

Type
Research Article
Copyright
Copyright © ASTIN Bulletin 2013 

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

de Jong, P. (2012) Modeling dependence between loss triangles using copula. North American Actuarial Journal, 16 (1), 7486.CrossRefGoogle Scholar
Fang, K., Kotz, S. and Ng, K. (2003) Symmetric Multivariate and Related Distributions. London, England: Chapman & Hall.Google Scholar
Happ, S. and Wuthrich, M. (2013) Paid-incurred chain reserving method with dependence modeling. ASTIN Bulletin, 43 (1), 120.CrossRefGoogle Scholar
Hurvich, C. and Tsai, C. (1989) Regression and time series model selection in small samples. Biometrika, 76 (2), 297307.CrossRefGoogle Scholar
Joe, H. (2005) Asymptotic efficiency of the two-stage estimation method for copula-based models. Journal of Multivariate Analysis, 94 (2), 401419.CrossRefGoogle Scholar
Jørgensen, B. and De Souza, M. (1994) Fitting Tweedie's compound Poisson model to insurance claims data. Scandinavian Actuarial Journal, 1 (1), 6993.CrossRefGoogle Scholar
McQuarrie, A. (1999) A small-sample correction for the Schwarz SIC model selection criterion. Statistics & Probability Letters, 44 (1), 7986.CrossRefGoogle Scholar
Merz, M. and Wüthrich, M. (2009a) Combining chain-ladder and additive loss reserving methods for dependent lines of business. Variance, 3 (2), 270291.Google Scholar
Merz, M. and Wüthrich, M. (2009b) Prediction error of the multivariate additive loss reserving method for dependent lines of business. Variance, 3 (1), 131151.Google Scholar
Merz, M., Wüthrich, M. and Hashorva, E. (2013) Dependence modeling in multivariate claims run-off triangles. Annals of Actuarial Science, 7 (1), 325.CrossRefGoogle Scholar
Meyers, G. and Shi, P. (2011) The retrospective testing of stochastic loss reserve models. Casualty Actuarial Society E-Forum, Summer 2011, http://www.casact.org/pubs/forum/11sumforum/.Google Scholar
Peters, G., Shevchenko, P. and Wüthrich, M. (2009) Model uncertainty in claims reserving within Tweedie's compound Poisson models. ASTIN Bulletin, 39 (1), 133.CrossRefGoogle Scholar
Salzmann, R. and Wüthrich, M. (2012) Modeling accounting year dependence in runoff triangles. European Actuarial Journal, 2 (2), 227242.CrossRefGoogle Scholar
Shi, P. (2012) Multivariate longitudinal modeling of insurance company expenses. Insurance: Mathematics and Economics, 51 (1), 204215.Google Scholar
Shi, P., Basu, S. and Meyers, G. (2012) A Bayesian log-normal model for multivariate loss reserving. North American Actuarial Journal, 16 (1), 2951.CrossRefGoogle Scholar
Shi, P. and Frees, E. (2011) Dependent loss reserving using copulas. ASTIN Bulletin, 41 (2), 449486.Google Scholar
Smyth, G. and Jørgensen, B. (2002) Fitting Tweedie's compound Poisson model to insurance claims data: Dispersion modelling. ASTIN Bulletin, 32 (1), 143157.CrossRefGoogle Scholar
Sugiura, N. (1978) Further analysis of the data by Akaike's information criterion and the finite corrections. Communications in Statistics: Theory and Methods, 7 (1), 1326.CrossRefGoogle Scholar
Sun, J., Frees, E. and Rosenberg, M. (2008) Heavy-tailed longitudinal data modeling using copulas. Insurance Mathematics and Economics, 42 (2), 817830.CrossRefGoogle Scholar
Tweedie, M. (1984) An index which distinguishes between some important exponential families. In Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference (eds. Ghosh, J. and Roy, J.), pp. 579604. Calcutta, India: Indian Statistical Institute.Google Scholar
Wüthrich, M. (2003) Claims reserving using Tweedie's compound Poisson model. ASTIN Bulletin, 33 (2), 331346.CrossRefGoogle Scholar
Wüthrich, M. (2012) Discussion of “A Bayesian log-normal model for multivariate loss reserving''. North America Actuarial Journal, 16 (3), 398401.Google Scholar
Wüthrich, M. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Chichester, England: John Wiley & Sons.Google Scholar
Zhang, Y. (2010) A general multivariate chain ladder model. Insurance: Mathematics and Economics, 46 (3), 588599.Google Scholar
17
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A COPULA REGRESSION FOR MODELING MULTIVARIATE LOSS TRIANGLES AND QUANTIFYING RESERVING VARIABILITY
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

A COPULA REGRESSION FOR MODELING MULTIVARIATE LOSS TRIANGLES AND QUANTIFYING RESERVING VARIABILITY
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

A COPULA REGRESSION FOR MODELING MULTIVARIATE LOSS TRIANGLES AND QUANTIFYING RESERVING VARIABILITY
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *