英文标题：
《Modulated Information Flows in Financial Markets》
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作者：
Edward Hoyle, Andrea Macrina, Levent A. Meng\\\"ut\\\"urk
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最新提交年份：
2020
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英文摘要：
  We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional L\\\'evy random bridge over a random point field, our framework relates the discovery of relevant new information sources to jumps in conditional expectation martingales. In the canonical Brownian random bridge case, we show that the underlying measure-valued process follows jump-diffusion dynamics, where the jumps are governed by information switches. The dynamic representation gives rise to a set of stochastically-linked Brownian motions on random time intervals that capture evolving information states, as well as to a state-dependent stochastic volatility evolution with jumps. The nature of information flows usually exhibits complex behaviour, however, we maintain analytic tractability by introducing what we term the effective and complementary information processes, which dynamically incorporate active and inactive information, respectively. As an application, we price a financial vanilla option, which we prove is expressed by a weighted sum of option values based on the possible state configurations at expiry. This result may be viewed as an information-based analogue of Merton\'s option price, but where jump-diffusion arises endogenously. The proposed information flows also lend themselves to the quantification of asymmetric informational advantage among competitive agents, a feature we analyse by notions of information geometry.
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中文摘要：
我们建立了连续时间的信息流模型，这些信息流由许多在随机时间打开和关闭的信息源生成。通过调制随机点场上的多维L拞evy随机桥，我们的框架将相关新信息源的发现与条件期望鞅中的跳跃联系起来。在正则布朗随机桥的情况下，我们证明了潜在的测度值过程遵循跳跃扩散动力学，其中跳跃由信息开关控制。动态表示产生了一组随机时间间隔上随机关联的布朗运动，这些布朗运动捕捉到了演化的信息状态，以及一个与状态相关的随机波动率演化和跳跃。信息流的性质通常表现出复杂的行为，然而，我们通过引入我们所称的有效和补充信息过程来保持分析的可跟踪性，这些过程分别动态地包含主动和非主动信息。作为一个应用，我们为一个金融普通期权定价，我们证明该期权由基于到期时可能的状态配置的期权值的加权和表示。这一结果可能被视为默顿期权价格的基于信息的类似物，但跳跃扩散是内生的。所提出的信息流也有助于量化竞争主体之间的不对称信息优势，这是我们通过信息几何的概念分析的一个特征。
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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