On Capital Allocation for a Risk Measure Derived from Ruin Theory

Guusje Delsing, Michel Mandjes, Peter Spreij and Erik Winands

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Abstract: 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 value-at-risk (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.

Date: 2021-03
New Economics Papers: this item is included in nep-rmg
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