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摘要翻译：
利用Peng([24])提出的G框架，研究了不确定条件下欧式未定权益的时间一致动态定价机制。考虑一个由无风险资产和有风险股票组成的金融市场，其价格过程为几何广义G-布朗运动，其特征是股票价格过程的漂移不确定性和波动不确定性。利用G-框架中的技术，我们证明了资产的风险溢价是不确定的，并且服从最大分布。由g-热方程的粘度解定义了一个时间一致的g-期望。利用时间一致的G期望，定义了索赔的G动态定价机制。我们证明了G动态定价机制是买卖马尔可夫动态定价机制。推导了完全非线性偏微分方程来描述索赔的出价（问）价过程。给出了非线性偏微分方程的单调隐式特征有限差分格式，构造了非线性迭代格式，并对不确定性条件下未定权益的出价（问）价进行了仿真。
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英文标题：
《Time Consistent Bid-Ask Dynamic Pricing Mechanisms for Contingent Claims
and Its Numerical Simulations 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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英文摘要：
We study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng ([24]). We consider a financial market consisting of a riskless asset and a risky stock with price process modelled by a geometric generalized G-Brownian motion, which features the drift uncertainty and volatility uncertainty of the stock price process. Using the techniques on G-framework we show that the risk premium of the asset is uncertain and distributed with maximum distribution. A time consistent G-expectation is defined by the viscosity solution of the G-heat equation. Using the time consistent G-expectation we define the G dynamic pricing mechanism for the claim. We prove that G dynamic pricing mechanism is the bid-ask Markovian dynamic pricing mechanism. The full nonlinear PDE is derived to describe the bid (resp. ask) price process of the claim. Monotone implicit characteristic finite difference schemes for the nonlinear PDE are given, nonlinear iterative schemes are constructed, and the simulations of the bid (resp. ask) prices of contingent claims under uncertainty are implemented.
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PDF链接：
https://arxiv.org/pdf/1111.4298
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