摘要翻译：
我们解决了Heston随机扩散模型的逃逸问题。我们得到了生存概率（这有助于解决完全逃逸问题）和平均退出时间的精确表达式。我们还对波动率进行平均，以便在不考虑波动率的情况下单独解决回报问题。我们根据波动率的无量纲正常水平--出现在Heston模型中的三个参数的比率--来研究这些结果，并在几个症状限制下分析它们的形式。因此，例如，我们表明，平均退出时间随大跨度呈二次增长，而对于小跨度，增长随正常水平的值而系统地变慢。我们将我们的结果与Wiener过程的结果进行了比较，表明随机波动性假设以一种明显矛盾的方式增加了存活率，延长了逃逸时间。
---
英文标题：
《The escape problem under stochastic volatility: the Heston model》
---
作者：
Jaume Masoliver, Josep Perello
---
最新提交年份：
2008
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
--
一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
--
一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
--

---
英文摘要：
  We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility --a ratio of the three parameters that appear in the Heston model-- and analyze their form in several assymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.
---
PDF链接：
https://arxiv.org/pdf/0807.1014