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Dependence Modelling in Insurance via Copulas with Skewed Generalised Hyperbolic Marginals

Vitali Alexeev (), Ignatieva Katja () and Liyanage Thusitha
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Ignatieva Katja: School of Risk and Actuarial Studies, Business School, UNSW Australia, Sydney, NSW 2052, Australia
Liyanage Thusitha: Portfolio and Market Risk Management Department, Commonwealth Bank of Australia, Sydney, NSW 2000, Australia

Studies in Nonlinear Dynamics & Econometrics, 2021, vol. 25, issue 2, 20

Abstract: This paper investigates dependence among insurance claims arising from different lines of business (LoBs). Using bivariate and multivariate portfolios of losses from different LoBs, we analyse the ability of various copulas in conjunction with skewed generalised hyperbolic (GH) marginals to capture the dependence structure between individual insurance risks forming an aggregate risk of the loss portfolio. The general form skewed GH distribution is shown to provide the best fit to univariate loss data. When modelling dependency between LoBs using one-parameter and mixture copula models, we favour models that are capable of generating upper tail dependence, that is, when several LoBs have a strong tendency to exhibit extreme losses simultaneously. We compare the selected models in their ability to quantify risks of multivariate portfolios. By performing an extensive investigation of the in- and out-of-sample Value-at-Risk (VaR) forecasts by analysing VaR exceptions (i.e. observations of realised portfolio value that are greater than the estimated VaR), we demonstrate that the selected models allow to reliably quantify portfolio risk. Our results provide valuable insights with regards to the nature of dependence and fulfils one of the primary objectives of the general insurance providers aiming at assessing total risk of an aggregate portfolio of losses when LoBs are correlated.

Keywords: copula; dependence modelling; insurance losses; skewed generalised hyperbolic distribution (search for similar items in EconPapers)
JEL-codes: C15 C46 G22 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/snde-2018-0094

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