cad a22 4500 317086081 20190416140649.0 cr unu---uuuuu 140624e201311 xx s 000 0 eng 10.1007/s00780-013-0220-9 doi (ZORA)oai:www.zora.uzh.ch:96662 330 ddc Farkas Walter Beyond cash-additive risk measures: When changing the numeraire fails [Elektronische Daten] [Walter Farkas, Pablo Koch-Medina, Cosimo-Andrea Munari] closedAccess eu-repo 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. Department of Banking and Finance zora Koch-Medina Pablo joint author Munari Cosimo-Andrea joint author Finance and Stochastics 18(1):145-173 https://www.zora.uzh.ch/96662 text/html WWW-Backlink auf das Repository Onlinezugriff via WWW text/html http://link.springer.com/article/10.1007%2Fs00780-013-0220-9 ZORA 1 Journal Article PeerReviewed zora ZORA 856 40 https://www.zora.uzh.ch/96662 text/html WWW-Backlink auf das Repository ZORA 856 42 Onlinezugriff via WWW text/html http://link.springer.com/article/10.1007%2Fs00780-013-0220-9 ZORA 100 1- Farkas Walter ZORA 700 1- Koch-Medina Pablo joint author ZORA 700 1- Munari Cosimo-Andrea joint author ZORA 773 0- Finance and Stochastics 18(1):145-173 SWISSBIB 317086081 BK010053 XK010053 XK010000 ZORA ZORA ZORA Journal Article closedAccess