The starting point and focal point of this present monograph is continuous-time stochastic processes allowing for jumps. Most textbooks on mathematical finance are limited to diffusion-type setups, which cannot easily account for abrupt price movements. Such changes, however, play an important role in real markets, which is why models with jumps have become an established tool in the statistics and mathematics of finance. Just as importantly, purely discontinuous processes lead to a much wider variety of, at the same time flexible and tractable, models. For example, their marginal laws are often known explicitly, which is typically not the case for diffusions.

这本专著的出发点和焦点是连续时间随机过程。大多数关于数学金融学的教科书都局限于扩散型的设置，这很难解释价格的突然变动。然而，这种变化在实际市场中发挥着重要作用，这就是为什么带跳跃的模型已经成为统计学和金融数学。同样重要的是，纯粹的不连续过程导致了更广泛的多样性，同时灵活和易于处理的模型。例如，它们的边际定律通常是明确知道的，而扩散通常不是这样。