英文标题：
《G-consistent price system and bid-ask pricing for European contingent
  claims under Knightian uncertainty》
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作者：
Wei Chen
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最新提交年份：
2013
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英文摘要：
  The target of this paper is to consider model the risky asset price on the financial market under the Knightian uncertainty, and pricing the ask and bid prices of the uncertain risk. We use the nonlinear analysis tool, i.e., G-frame work [26], to construct the model of the risky asset price and bid-ask pricing for the European contingent claims under Knightian uncertain financial market. Firstly, we consider the basic risky asset price model on the uncertain financial market, which we construct here is the model with drift uncertain and volatility uncertain. We describe such model by using generalized G-Brownian motion and call it as G-asset price system. We present the uncertain risk premium which is uncertain and distributed with maximum distribution. We derive the closed form of bid-ask price of the European contingent claim against the underlying risky asset with G-asset price system as the discounted conditional G-expecation of the claim, and the bid and ask prices are the viscosity solutions to the nonlinear HJB equations.Furthermore, we consider the main part of this paper, i.e., consider the risky asset on the Knightian uncertain financial market with the price fluctuation shows as continuous trajectories. We propose the G-conditional full support condition by using uncertain capacity, and the risky asset price path satisfying the G-conditional full support condition could be approximated by its G-consistent asset price systems. We derive that the bid and ask prices of the European contingent claim against such risky asset under uncertain can be expressed by discounted of some conditional G-expectation of the claim. We give examples, such as G-Markovian processes and the geometric fractional G-Brownian motion [9], satisfying the G-conditional full support condition.
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中文摘要：
本文的目的是考虑在Knightian不确定性下金融市场上风险资产的价格模型，并对不确定性风险的买卖价格进行定价。我们使用非线性分析工具，即G-frame work[26]，构建了Knightian不确定金融市场下欧洲未定权益的风险资产价格和买卖定价模型。首先，我们考虑了不确定金融市场上的基本风险资产价格模型，我们构造了一个具有漂移不确定性和波动不确定性的模型。我们用广义G-布朗运动来描述这种模型，并称之为G-资产价格系统。我们给出了不确定的风险溢价，它是不确定的，并且以最大分布分布分布。利用G-资产价格系统作为标的风险资产的贴现条件G-支出，推导了欧洲未定权益的买卖价格的封闭形式，买卖价格是非线性HJB方程的粘性解。此外，我们还考虑了本文的主要部分，即考虑价格波动呈连续轨迹的Knightian不确定金融市场上的风险资产。我们利用不确定容量提出了G-条件完全支持条件，满足G-条件完全支持条件的风险资产价格路径可以用其G-相容的资产价格系统来近似。我们推导出，在不确定条件下，针对此类风险资产的欧洲未定权益的出价和要价可以通过对索赔的某些条件G-期望的折扣来表示。我们给出了满足G-条件全支撑条件的例子，如G-马尔可夫过程和几何分数G-布朗运动[9]。
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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：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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