摘要翻译：
Peng[41]提出了不确定条件下度量风险的G-框架。本文定义了分数G-布朗运动(fGBm)。分数G-布朗运动是一个零均值的中心G-高斯过程，在亚线性意义上具有平稳增量，Hurst指数$h\\in（0,1)$。该过程具有平稳增量、自相似性和亚线性意义上的长区间依赖性质。这些性质使分数G-布朗运动成为数学金融学中一个合适的驱动过程。利用紧支撑小波构造fGBm的小波分解。我们发展了分数G-white噪声理论，定义了G-IT-O-Wick随机积分，建立了分数G-IT-O公式和分数G-Clark-Ocone公式，导出了G-Girsanov定理。为了应用G白噪声理论，我们考虑了由FGBM驱动的G-Wick-It\\o型SDE模型的金融市常fGBm模型下的金融资产价格具有波动性不确定性，利用G-Girsanov定理和G-Clark-Ocone定理，我们得到了贴现后的欧式未定权益的次线性期望是该权益的买卖价格。
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英文标题：
《Fractional G-White Noise Theory, Wavelet Decomposition for Fractional
G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under
Uncertainty》
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作者：
Wei Chen
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最新提交年份：
2013
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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英文摘要：
G-framework is presented by Peng [41] for measure risk under uncertainty. In this paper, we define fractional G-Brownian motion (fGBm). Fractional G-Brownian motion is a centered G-Gaussian process with zero mean and stationary increments in the sense of sub-linearity with Hurst index $H\\in (0,1)$. This process has stationary increments, self-similarity, and long rang dependence properties in the sense of sub-linearity. These properties make the fractional G-Brownian motion a suitable driven process in mathematical finance. We construct wavelet decomposition of the fGBm by wavelet with compactly support. We develop fractional G-white noise theory, define G-It\\^o-Wick stochastic integral, establish the fractional G-It\\^o formula and the fractional G-Clark-Ocone formula, and derive the G-Girsanov\'s Theorem. For application the G-white noise theory, we consider the financial market modelled by G-Wick-It\\^o type of SDE driven by fGBm. The financial asset price modelled by fGBm has volatility uncertainty, using G-Girsanov\'s Theorem and G-Clark-Ocone Theorem, we derive that sublinear expectation of the discounted European contingent claim is the bid-ask price of the claim.
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