英文标题：
《A Gaussian Markov alternative to fractional Brownian motion for pricing
financial derivatives》
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作者：
Daniel Conus and Mackenzie Wildman
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最新提交年份：
2016
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英文摘要：
Replacing Black-Scholes\' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial market. We present the development, testing, and implementation of a simplified alternative to using fractional Brownian motion for pricing derivatives. By relaxing the assumption of past independence of Brownian motion but retaining the Markovian property, we are developing a competing model that retains the mathematical simplicity of the standard Black-Scholes model but also has the improved accuracy of allowing for past dependence. This is achieved by replacing Black-Scholes\' underlying process, Brownian motion, with a particular Gaussian Markov process, proposed by Vladimir Dobri\\\'{c} and Francisco Ojeda.
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中文摘要：
用分数布朗运动代替Black-Scholes的驱动过程，可以将过去对股票价格的依赖性纳入其中，但面临一些重大下跌，包括在金融市场实施套利。我们将开发、测试和实现一种简化的替代方法，以替代使用分数布朗运动为衍生工具定价的方法。通过放宽布朗运动过去独立性的假设，但保留马尔可夫性质，我们正在开发一个竞争模型，该模型保留了标准Black-Scholes模型的数学简单性，但也提高了考虑过去依赖性的准确性。这是通过用弗拉基米尔·多布里（Vladimir Dobri）{c}和弗朗西斯科·奥杰达（Francisco Ojeda）提出的一种特殊的高斯-马尔可夫过程取代布莱克-斯科尔斯（Black-Scholes）的基本过程布朗运动来实现的。
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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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