英文标题：
《On the martingale property in the rough Bergomi model》
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作者：
Paul Gassiat
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最新提交年份：
2019
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英文摘要：
We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussian process. We show that the stock price is a true martingale if and only if the correlation $\\rho$ between the driving Brownian motions of the stock and the volatility is nonpositive. We also show that for each $\\rho<0$ and $m> \\frac{1}{{1-\\rho^2}}$, the $m$-th moment of the stock price is infinite at each positive time.
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中文摘要：
我们考虑一类分数阶随机波动率模型（包括所谓的粗糙Bergomi模型），其中波动率是分数阶高斯过程的超线性函数。我们证明了股票价格是真鞅当且仅当股票的驱动布朗运动与波动率之间的相关性为非正时。我们还表明，对于每一个$\\rho<0$和$\\m>\\frac{1}{{1-\\rho^2}}}美元，股价的第m$时刻在每个正时间是无限的。
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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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