Bargès, Mathieu; Cossette, Hélène; Marceau, Étienne TVaR-based capital allocation with copulas. (English) Zbl 1231.91141 Insur. Math. Econ. 45, No. 3, 348-361 (2009). Summary: Because of regulation projects from control organisations such as the European Solvency II reform and recent economic events, insurance companies need to consolidate their capital reserve with coherent amounts allocated to the whole company and to each line of business. The present study considers an insurance portfolio consisting of several lines of risk which are linked by a copula and aims to evaluate not only the capital allocation for the overall portfolio but also the contribution of each risk over their aggregation. We use the tail value at risk (TVaR) as risk measure. The handy form of the FGM copula permits an exact expression for the TVaR of the sum of the risks and for the TVaR-based allocations when claim amounts are exponentially distributed and distributed as a mixture of exponentials. We first examine the bivariate model and then the multivariate case. We also show how to approximate the TVaR of the aggregate risk and the contribution of each risk when using any copula. Cited in 37 Documents MSC: 91B30 Risk theory, insurance (MSC2010) 91G10 Portfolio theory 60E05 Probability distributions: general theory 62H05 Characterization and structure theory for multivariate probability distributions; copulas Keywords:capital allocation; tail value at risk; dependence models; copulas; discretization methods PDFBibTeX XMLCite \textit{M. Bargès} et al., Insur. Math. Econ. 45, No. 3, 348--361 (2009; Zbl 1231.91141) Full Text: DOI References: [1] Acerbi, C., Nordio, C., Sirtori, C., 2001. Expected shortfall as a tool for financial risk management. Working Paper; Acerbi, C., Nordio, C., Sirtori, C., 2001. Expected shortfall as a tool for financial risk management. 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