- Journal Article
Rights / licenseIn Copyright - Non-Commercial Use Permitted
We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a risk-free bond, on the grounds that the general case can be reduced to the cash-additive case by a change of numéraire. However, discounting does not work in all financially relevant situations, especially when the eligible asset is a defaultable bond. In this paper, we fill this gap by allowing general eligible assets. We provide a variety of finiteness and continuity results for the corresponding risk measures and apply them to risk measures based on value-at-risk and tail value-at-risk on L p spaces, as well as to shortfall risk measures on Orlicz spaces. We pay special attention to the property of cash subadditivity, which has been recently proposed as an alternative to cash additivity to deal with defaultable bonds. For important examples, we provide characterizations of cash subadditivity and show that when the eligible asset is a defaultable bond, cash subadditivity is the exception rather than the rule. Finally, we consider the situation where the eligible asset is not liquidly traded and the pricing rule is no longer linear. We establish when the resulting risk measures are quasiconvex and show that cash subadditivity is only compatible with continuous pricing rules. Show more
Journal / seriesFinance and Stochastics
Pages / Article No.
SubjectRisk measures; Acceptance sets; General eligible assets; Defaultable bonds; Cash subadditivity; Quasiconvexity; Value-at-risk; Tail value-at-risk; Shortfall risk
Organisational unit03658 - Schweizer, Martin / Schweizer, Martin
NotesIt was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
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