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Beyond correlation: Recent developments in the modelling of claims dependenciesBenjamin Avanzi, School of Risk and Actuarial Studies, UNSW and Département de Mathématiques et de Statistique, Université de MontréalGreg Taylor, Bernard Wong,School of Risk and Actuarial Studies, UNSWInsights, 5 April 2016
Beyond correlation: Recent developments in the modelling of claims dependenciesContext
Actuarial: Dependence modelling
Our team: Linkage project
On correlations
Introduction
Practice
Correlation pitfalls
So what?
Dependence modelling approaches
Implicit vs explicit modelling of dependence
Micro vs Macro modelling
Discussion
Recent developments and case studies
Multivariate Tweedie reserving model
Lévy Copulas - dependence modelling for Lévy processes Cox process approach to the micro-modelling of insurance claimsDependence modelling using Cox processes
Summary and Conclusions
List of (some) recent references
Details of all references
1/61 Beyond correlation: Recent developments in the modelling of claims dependenciesContext
Context
Actuarial: Dependence modelling
Our team: Linkage project
On correlations
Introduction
Practice
Correlation pitfalls
So what?
Dependence modelling approaches
Implicit vs explicit modelling of dependence
Micro vs Macro modelling
Discussion
Recent developments and case studies
Multivariate Tweedie reserving model
Lévy Copulas - dependence modelling for Lévy processes Cox process approach to the micro-modelling of insurance claimsDependence modelling using Cox processes
Summary and Conclusions
List of (some) recent references
Details of all references
2/61 Beyond correlation: Recent developments in the modelling of claims dependenciesContext
Actuarial: Dependence modelling
Context
Actuarial: Dependence modelling
Our team: Linkage project
On correlations
Introduction
Practice
Correlation pitfalls
So what?
Dependence modelling approaches
Implicit vs explicit modelling of dependence
Micro vs Macro modelling
Discussion
Recent developments and case studies
Multivariate Tweedie reserving model
Lévy Copulas - dependence modelling for Lévy processes Cox process approach to the micro-modelling of insurance claimsDependence modelling using Cox processes
Summary and Conclusions
List of (some) recent references
Details of all references
2/61 Beyond correlation: Recent developments in the modelling of claims dependenciesContext
Actuarial: Dependence modelling
Significance of stochastic dependence
Practically speaking, dependence structures can have a major impact in several areas of the business of an insurance company (see also IAA, 2004, 2009), including I determining actuarial reserves (IBNR): quantile, or central estimate (the mean) plus margin; I determining a risk based capital for solvency assessment In all cases, structures with less than perfect dependence will lead to diversification b enefits , whose accurate estimation is crucial for I capital efficiency (not underestimate); I solvency of the insurance company (not overestimate). 2/61 Beyond correlation: Recent developments in the modelling of claims dependenciesContext
Our team: Linkage project
Context
Actuarial: Dependence modelling
Our team: Linkage project
On correlations
Introduction
Practice
Correlation pitfalls
So what?
Dependence modelling approaches
Implicit vs explicit modelling of dependence
Micro vs Macro modelling
Discussion
Recent developments and case studies
Multivariate Tweedie reserving model
Lévy Copulas - dependence modelling for Lévy processes Cox process approach to the micro-modelling of insurance claimsDependence modelling using Cox processes
Summary and Conclusions
List of (some) recent references
Details of all references
3/61 Beyond correlation: Recent developments in the modelling of claims dependenciesContext
Our team: Linkage project
Modelling claim dependencies for the general insurance industry with economic capital in view: An innovative approach with stochastic processes "The project will develop progressive methods to b etterrep resent the fine, complex structures driving the significant dependencies relevant to the Enterprise Risk Management of general insurers Collaborative between, and jointly funded by Government, industry (Allianz, IAG, Suncorp) and academiaSee also
a rticlein the A ctuariesMagazine, August 2014 (A vanzi,Taylor, and Wong, 2014)back
3/61 Beyond correlation: Recent developments in the modelling of claims dependenciesOn correlations
Context
Actuarial: Dependence modelling
Our team: Linkage project
On correlations
Introduction
Practice
Correlation pitfalls
So what?
Dependence modelling approaches
Implicit vs explicit modelling of dependence
Micro vs Macro modelling
Discussion
Recent developments and case studies
Multivariate Tweedie reserving model
Lévy Copulas - dependence modelling for Lévy processes Cox process approach to the micro-modelling of insurance claimsDependence modelling using Cox processes
Summary and Conclusions
List of (some) recent references
Details of all references
4/61 Beyond correlation: Recent developments in the modelling of claims dependenciesOn correlations
Introduction
Context
Actuarial: Dependence modelling
Our team: Linkage project
On correlations
Introduction
Practice
Correlation pitfalls
So what?
Dependence modelling approaches
Implicit vs explicit modelling of dependence
Micro vs Macro modelling
Discussion
Recent developments and case studies
Multivariate Tweedie reserving model
Lévy Copulas - dependence modelling for Lévy processes Cox process approach to the micro-modelling of insurance claimsDependence modelling using Cox processes
Summary and Conclusions
List of (some) recent references
Details of all references
4/61 Beyond correlation: Recent developments in the modelling of claims dependenciesOn correlations
Introduction
At our last
'Insights" Session (Octob er2015) , we concluded: ICorrelation depends on your model
ICorrelation happens as a result of real phenomena
I The more of those phenomenons you can explain in your model, the less dependent your residuals will look like I We wiped away all correlation from the AUSI dataset I But what you can use to explain past data may not necessarily be available to explain (predict) the future I Correlation is all but one way of specifying dependenceSee also
I article in the Actuaries Magazine, September 2015 (Avanzi, Taylor, and Wong, 2015a) I article in BusinessThink, December 2015 (BusinessThink, 2015) I academic article in ASTIN Bulletin, in press (Avanzi, Taylor, and Wong, 2015b) 4/61 Beyond correlation: Recent developments in the modelling of claims dependenciesOn correlations
Introduction
Correlation
Definition:
IWe refer to 'Pearson correlation"
IThis is a measure of
linea r dep endence,which is symmetric around the mean IHence, it is tied to elliptical distributions
(Normal, Student) I In fact, it completely specifies the dependence structure ofNormal and Student distributions
Why then, could there be a need to move beyond correlation? 5/61 Beyond correlation: Recent developments in the modelling of claims dependenciesOn correlations
Practice
Context
Actuarial: Dependence modelling
Our team: Linkage project
On correlations
Introduction
Practice
Correlation pitfalls
So what?
Dependence modelling approaches
Implicit vs explicit modelling of dependence
Micro vs Macro modelling
Discussion
Recent developments and case studies
Multivariate Tweedie reserving model
Lévy Copulas - dependence modelling for Lévy processes Cox process approach to the micro-modelling of insurance claimsDependence modelling using Cox processes
Summary and Conclusions
List of (some) recent references
Details of all references
6/61 Beyond correlation: Recent developments in the modelling of claims dependenciesOn correlations
Practice
Risk margins
When calculating risk margins, usual practice would be to followthese steps:1Estimate the mean and variance of liability for each LoB;2Estimate the associated correlation matrix;3Hence estimate the mean and variance of the total liability
across all LoBs;4Assume some convenient distribution for this total liability, usually log normal;5Calculate the 75-percentile from this distribution. Frequent assumption for step [2] would be consistent with Bateup and Reed (2001) and/or Collings and White (2001). 6/61 Beyond correlation: Recent developments in the modelling of claims dependenciesOn correlations
Practice
Capital margins
When calculating (high percentile) capital margins, usual practicewould be to follow these steps:1Estimate the distribution of liability for each LoB;2Assume a copula across the LoBs, most commonlyt-copula;3Perform a multivariate simulation of liabilities for all LoBs;4Form the replicates of total liabilities across LoBs, and read off
required percentile. 7/61 Beyond correlation: Recent developments in the modelling of claims dependencies