This paper addresses allocation methodologies for a risk measure inherited from ruin theory. Specifically, we consider a dynamic value-at-risk (VaR) measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given threshold. We introduce an intuitively appealing, novel allocation method, with a focus on its application to capital reserves which are determined through the dynamic VaR measure. Various desirable properties of the presented approach are derived including a limit result when considering a large time horizon and the comparison with the frequently used gradient allocation method. In passing, we introduce a second allocation method and discuss its relation to the other allocation approaches. A number of examples illustrate the applicability and performance of the allocation approaches.

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Rabobank, Utrecht, the Netherlands
Insurance: Mathematics and Economics
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Delsing, G.A, Mandjes, M.R.H, Spreij, P.J.C, & Winands, E.M.M. (2022). On capital allocation for a risk measure derived from ruin theory. Insurance: Mathematics and Economics, 104, 76–98. doi:10.1016/j.insmatheco.2022.02.001