英文标题：
《Shot-Noise Processes in Finance》
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作者：
Thorsten Schmidt
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最新提交年份：
2016
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英文摘要：
  Shot-Noise processes constitute a useful tool in various areas, in particular in finance. They allow to model abrupt changes in a more flexible way than processes with jumps and hence are an ideal tool for modelling stock prices, credit portfolio risk, systemic risk, or electricity markets. Here we consider a general formulation of shot-noise processes, in particular time-inhomogeneous shot-noise processes. This flexible class allows to obtain the Fourier transforms in explicit form and is highly tractable. We prove that Markovianity is equivalent to exponential decay of the noise function. Moreover, we study the relation to semimartingales and equivalent measure changes which are essential for the financial application. In particular we derive a drift condition which guarantees absence of arbitrage. Examples include the minimal martingale measure and the Esscher measure.
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中文摘要：
散粒噪声过程在各个领域，特别是在金融领域，都是一种有用的工具。它们允许以比跳跃过程更灵活的方式对突变进行建模，因此是建模股票价格、信贷组合风险、系统风险或电力市场的理想工具。这里我们考虑散粒噪声过程的一般表达式，特别是时间非均匀散粒噪声过程。这个灵活的类允许以显式形式获得傅立叶变换，并且非常容易处理。我们证明了马尔可夫性等价于噪声函数的指数衰减。此外，我们还研究了半鞅与等价测度变化之间的关系，这对于金融应用至关重要。特别地，我们推导了一个漂移条件，该条件保证没有套利。示例包括最小鞅测度和Esscher测度。
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分类信息：

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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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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