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Group cohesion under individual regulatory constraints

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  • Delia Coculescu
  • Freddy Delbaen

Abstract

We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit, more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex cone. Because of these requirements, there are less incentives to operate under a group structure, as creating one single business unit, or altering the liability repartition among units, may allow to reduce the required capital. We analyse the possibilities for the group to benefit from a diversification effect and economise on the cost of capital. We define and study the risk measures that allow for any group to achieve the minimal capital, as if it were a single unit, without altering the liability of business units, and despite the individual admissibility constraints. We call these risk measures cohesive risk measures.

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  • Delia Coculescu & Freddy Delbaen, 2020. "Group cohesion under individual regulatory constraints," Papers 2010.01428, arXiv.org.
  • Handle: RePEc:arx:papers:2010.01428
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    References listed on IDEAS

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    1. Delia Coculescu & Freddy Delbaen, 2020. "Fairness principles for insurance contracts in the presence of default risk," Papers 2009.04408, arXiv.org.
    2. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    3. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
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