最大风险监测日期
Monitoring dates of maximal risk
摘要：
监控是指使用某种监视器或测量设备来观察系统随时间可能发生的任何变化。在本文中，我们制定了一个问题的监测日期的最大风险的财务状况。因此，我们将要观察的系统是从金融的情况中产生的。我们将使用的测量设备是一种时间一致的风险测量方法。本文的第一部分讨论了定义在空间Lp（F，R）中取值于L1（G，R）的条件凸风险测度的数值表示。这将允许我们考虑L1（R）中的时间一致凸风险度量。在本文的第二部分中，我们使用时间一致的凸风险度量，以定义一个抽象的问题，监测停时的最大风险。在鲁棒表示中所涉及的罚函数在最大风险首次被识别时定性地改变。我们从稳健统计学的角度来讨论这一现象。
英文摘要：
Monitoring means to observe a system for any changes which may occur over time, using a monitor or measuring device of some sort. In this paper we formulate a problem of monitoring dates of maximal risk of a financial position. Thus, the systems we are going to observe arise from situations in finance. The measuring device we are going to use is a time-consistent measure of risk. In the first part of the paper we discuss the numerical representation of conditional convex risk measures which are defined in a space Lp(F,R) and take values in L1(G,R). This will allow us to consider time-consistent convex risk measures in L1(R). In the second part of the paper we use a time-consistent convex risk measure in order to define an abstract problem of monitoring stopping times of maximal risk. The penalty function involved in the robust representation changes qualitatively the time when maximal risk is for the first time identified. A phenomenon which we discuss from the point of view of robust statistics.
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