超越现金附加风险度量：当改变数字失败时
Beyond cash-additive risk measures: when changing the numéraire fails
摘要：
我们讨论了代表金融机构需要筹集和投资于预先指定的合格资产以确保其资本充足的最低资本额的风险度量。大多数文献都侧重于现金加成风险计量，其中合格资产是无风险债券，理由是一般情况可以通过改变计数值而简化为现金加成情况。然而，贴现并不适用于所有与财务相关的情况，特别是当合格资产是可违约债券时。在本文中，我们填补了这一空白，允许一般合格的资产。我们提供了各种有限性和连续性的结果，相应的风险措施，并将其应用到风险的风险措施的基础上的风险值和尾值风险$L^p$空间，以及短缺风险措施Orlicz空间。我们特别注意现金次可加性的属性，这是最近提出的现金可加性的替代处理违约债券。对于重要的例子，我们提供了现金次可加性的特征，并表明，当合格的资产是一个违约债券，现金次可加性是例外，而不是规则。最后，我们考虑的情况下，合格的资产不是流动性交易和定价规则不再是线性的。我们建立了当由此产生的风险措施是拟凸的，并表明，现金次可加性是唯一兼容的连续定价规则。
英文摘要：
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 numeraire. However, discounting does not work in all financially relevant situations, typically when the eligible asset is a defaultable bond. In this paper we fill this gap allowing for 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
