Jump processes
Jump processes
复制标题
跳转进程
DOI：
10.1002/9780470061602.eqf19021
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
E. Eberlein
中科院分区：
文献类型：
--
作者：
E. Eberlein
尽管在历史上，数学金融中的模型是基于布朗运动的，因此是具有连续价格路径的模型，但跳跃过程现在在金融的所有领域发挥着关键作用(例如，见[5])。这种转移到一类新的过程的一个原因是，由于它们的分布特性，扩散在许多情况下不能提供经验观察到的事实的真实图景。另一个原因是由于半鞅理论的发展和计算能力的发展，在理解和处理跳跃过程方面取得了巨大的进步。最简单的跳跃过程是只有一次跳跃的过程。设T是随机时间--实际上是关于由过滤(Ft)t≥0给出的信息结构的停止时间-则Xt=1l{T≤t}(t≥0)(1)
Although historically models in mathematical finance were based on Brownian motion and thus are models with continuous price paths, jump processes play now a key role across all areas of finance (see e.g. [5]). One reason for this move into a new class of processes is that because of their distributional properties diffusions in many cases cannot provide a realistic picture of empirically observed facts. Another reason is the enormous progress which has been made in understanding and handling jump processes due to the development of semimartingale theory on one side and of computational power on the other side. The simplest jump process is a process with just one jump. Let T be a random time – actually a stopping time with respect to an information structure given by a filtration (Ft)t≥0 – then Xt = 1l{T≤t} (t ≥ 0) (1)