论文标题
日志 - 熟练性：建模金融市场的新概念
Log-ergodicity: A New Concept for Modeling Financial Markets
论文作者
论文摘要
尽管金融模型通常违反了崇高性，但观察市场中的千古行为并不罕见。政策制定者和市场参与者控制关键和紧急状态的市场行为，这导致一定程度的恶性，因为他们的行动是故意的。在本文中，我们定义了作用于正随机过程空间的参数算子，将一类正随机过程转换为平均值过程。有了这种机制，我们提取有关财务模型中隐藏的千古行为的数据，将其应用于数学金融，并为定价有意义的主张建立新的方法。我们提供了一些经验示例，并将结果与现有结果进行比较，以证明这种新方法的功效。
Although financial models violate ergodicity in general, observing the ergodic behavior in the markets is not rare. Policymakers and market participants control the market behavior in critical and emergency states, which leads to some degree of ergodicity as their actions are intentional. In this paper, we define a parametric operator that acts on the space of positive stochastic processes, transforming a class of positive stochastic processes into mean-ergodic processes. With this mechanism, we extract the data regarding the ergodic behavior hidden in the financial model, apply it to mathematical finance, and establish a novel method for pricing contingent claims. We provide some empirical examples and compare the results with existing ones to demonstrate the efficacy of this new approach.
