On capital allocation for a risk measure derived from ruin theory

G.A. Delsing, M.R.H. Mandjes, P.J.C. Spreij and E.M.M. Winands

Insurance: Mathematics and Economics, 2022, vol. 104, issue C, 76-98

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 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.

Keywords: Risk capital allocation; Gradient allocation method; Value-at-risk (VaR); Ruin probability; Insurance risk (search for similar items in EconPapers)
JEL-codes: C32 C69 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:104:y:2022:i:c:p:76-98

DOI: 10.1016/j.insmatheco.2022.02.001

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