动态谱风险测度、极限定理与最优投资组合
On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation
摘要：
本文提出了连续时间动态谱风险测度的概念。采用Poisson随机测度设置，我们定义了这类动态相干风险测度的倒向随机微分方程。通过建立泛函极限定理，我们证明了DSRs可以被认为是迭代谱风险测度的（强）时间相容的连续时间扩展，迭代谱风险测度是通过沿着给定的时间网格迭代给定的谱风险测度（如期望短缺）而得到的.具体来说，我们证明了任何DSR出现在有限的一系列这样的迭代谱风险措施驱动的晶格随机游动，在适当的缩放和消失的时间和空间的网格步长。为了说明其在金融优化问题中的应用，我们分析了DSR下的动态投资组合优化问题。
英文摘要：
In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may be considered to be (strongly) time-consistent continuous-time extensions of iterated spectral risk-measures, which are obtained by iterating a given spectral risk-measure (such as Expected Shortfall) along a given time-grid. Specifically, we demonstrate that any DSR arises in the limit of a sequence of such iterated spectral risk-measures driven by lattice-random walks, under suitable scaling and vanishing time- and spatial-mesh sizes. To illustrate its use in financial optimisation problems, we analyse a dynamic portfolio optimisation problem under a DSR.
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