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On Capital Allocation for a Risk Measure Derived from Ruin Theory

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  • Guusje Delsing
  • Michel Mandjes
  • Peter Spreij
  • Erik Winands

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.

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  • Guusje Delsing & Michel Mandjes & Peter Spreij & Erik Winands, 2021. "On Capital Allocation for a Risk Measure Derived from Ruin Theory," Papers 2103.16264, arXiv.org.
    • Handle: RePEc:arx:papers:2103.16264
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    References listed on IDEAS

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