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TVaR-based capital allocation with copulas

Author

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  • Mathieu Bargès

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon, Ecole d'Actuariat - ULaval - Université Laval [Québec])

  • Hélène Cossette

    (Ecole d'Actuariat - ULaval - Université Laval [Québec])

  • Etienne Marceau

    (Ecole d'Actuariat - ULaval - Université Laval [Québec])

Abstract

Because of regulation projects from control organizations 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.

Suggested Citation

  • Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    • Handle: RePEc:hal:wpaper:hal-00431265
    Note: View the original document on HAL open archive server: https://hal.science/hal-00431265
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    References listed on IDEAS

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