In this article, we extend the framework of monetary risk measures for stochastic processes to account for heavy tailed distributions of random cash flows evolving over a fixed trading horizon. To this end, we transfer the \(L^p\)-duality underlying the representation of monetary risk measures to a more flexible Orlicz duality, in spaces of stochastic processes modelling random future evolution of financial values in continuous time over a finite horizon. This contributes, on the one hand, to the theory of real-valued monetary risk measures for processes and, on the other hand, supports a new representation of acceptability indices of financial performance.

中文翻译：

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通过 Orlicz 对偶的随机过程的货币风险度量

在本文中，我们扩展了随机过程的货币风险度量框架，以解释在固定交易范围内演变的随机现金流的重尾分布。为此，我们将表示货币风险度量的\(L^p\) -对偶性转移到更灵活的 Orlicz 对偶性，在随机过程空间中，对有限范围内连续时间内金融价值的随机未来演变进行建模。一方面，这有助于流程的实值货币风险度量理论，另一方面，支持财务绩效可接受指数的新表示。