市场波动性下的动态风险度量：在Bochner-勒贝格空间中
Dynamic risk measures for fluctuations in market volatility under Bochner-Lebesgue spaces
AI总结：
本文在Bochner-勒贝格空间中提出动态风险度量方法，用于捕捉金融市场波动性变化的复杂性。
摘要：
从全球金融危机到最近由地缘政治紧张和公共卫生危机引发的动荡，金融市场的风险波动性显著增加。这突显了需要能够捕捉市场波动复杂性和高度波动性的全面风险度量的必要性。这种需求不仅对新金融资产至关重要，也对传统金融市场在快速变化的金融环境和全球格局下至关重要。在本文中，我们考虑了在特殊空间$ L^{p(\cdot)} $上的风险度量，其中变量指数$ p(\cdot) $不再像传统风险度量空间$ L^{p} $中的给定实数那样固定，而是作为反映金融市场波动性潜在波动的随机变量。通过进一步发展与这一类风险度量相关的公理，我们还为它们建立了对偶表示。
英文摘要：
Starting from the global financial crisis to the more recent disruptions brought about by geopolitical tensions and public health crises, the volatility of risk in financial markets has increased significantly. This underscores the necessity for comprehensive risk measures capable of capturing the complexity and heightened fluctuations in market volatility. This need is crucial not only for new financial assets but also for the traditional financial market in the face of a rapidly changing financial environment and global landscape. In this paper, we consider the risk measures on a special space $L^{p(\cdot)}$, where the variable exponent $p(\cdot)$ is no longer a given real number as in the conventional risk measure space $L^{p}$, but rather a random variable reflecting potential fluctuations in volatility within financial markets. Through further development of axioms related to this class of risk measures, we also establish dual representations for them.
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。
