英文标题：
《Scalar multivariate risk measures with a single eligible asset》
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作者：
Zachary Feinstein, Birgit Rudloff
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最新提交年份：
2021
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英文摘要：
In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variables as (equivalent) martingale measures and prices consistent with the market model. Then, these dual representations are used to obtain the main results of this paper on time consistency for scalar risk measures in markets with frictions. It is well known from the superhedging risk measure in markets with transaction costs, as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied. We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process. We will prove the equivalence of this weaker notion of time consistency and a certain type of backward recursion with respect to the underlying risk measure with a fixed consistent pricing process. Several examples are given, with special emphasis on the superhedging risk measure.
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中文摘要：
本文给出了具有交易成本的市场中标量风险测度的结果。此类风险度量被定义为现金资产的最低资本要求。首先，给出了这类风险测度的对偶表示的一些结果，特别强调了对偶变量的空间，如（等价）鞅测度和与市场模型一致的价格。然后，利用这些对偶表示得到了本文关于有摩擦市场中标量风险度量的时间一致性的主要结果。从具有交易成本的市场中的超边缘风险度量，如Jouini和Kallal（1995）、Roux和Zastawniak（2016）以及Loehne和Rudloff（2014），众所周知，通常的时间一致性标量概念太强，不能令人满意。我们将证明，可以定义一个较弱的时间一致性概念，它对应于通常的标量时间一致性，但在任何固定的一致定价过程下。我们将证明这种较弱的时间一致性概念和某种类型的向后递归对于具有固定一致定价过程的潜在风险度量的等价性。给出了几个例子，特别强调了超边缘风险度量。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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