标题： 金融中的 shot-noise 过程 显示英文标题

标题： Shot-Noise Processes in Finance

摘要： 冲激噪声过程在多个领域中构成了一种有用的工具，特别是在金融领域。 与具有跳跃的随机过程相比，它们能够以更灵活的方式建模突变变化，因此是建模股票价格、信用组合风险、系统性风险或电力市场等的理想工具。 在这里，我们考虑了冲激噪声过程的一种一般形式，特别是非齐次时间冲激噪声过程。 这一灵活的类可以显式地获得傅里叶变换，并且高度可处理。 我们证明了马尔可夫性等价于噪声函数的指数衰减。 此外，我们研究了与半鞅和等价测度变化的关系，这些对于金融应用至关重要。 特别是，我们推导出一个保证不存在套利的漂移条件。 例子包括最小鞅测度和 Esscher 测度。 显示英文摘要

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.