On Capital Allocation for a Risk Measure Derived from Ruin Theory
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.
Keywords
Cite
@article{arxiv.2103.16264,
title = {On Capital Allocation for a Risk Measure Derived from Ruin Theory},
author = {Guusje Delsing and Michel Mandjes and Peter Spreij and Erik Winands},
journal= {arXiv preprint arXiv:2103.16264},
year = {2021}
}