英文标题：
《Robust valuation and risk measurement under model uncertainty》
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作者：
Yuhong Xu
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最新提交年份：
2014
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英文摘要：
Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets and option markets with uncertain prior distribution are established by Peng\'s G-stochastic calculus. The process of stock price is described by generalized geometric G-Brownian motion in which the mean uncertainty may move together with or regardless of the volatility uncertainty. On the hedging market, the upper price of an (exotic) option is derived following the Black-Scholes-Barenblatt equation. It is interesting that the corresponding Barenblatt equation does not depend on the risk preference of investors and the mean-uncertainty of underlying stocks. Hence under some appropriate sublinear expectation, neither the risk preference of investors nor the mean-uncertainty of underlying stocks pose effects on our super and subhedging strategies. Appropriate definitions of arbitrage for super and sub-hedging strategies are presented such that the super and sub-hedging prices are reasonable. Especially the condition of arbitrage for sub-hedging strategy fills the gap of the theory of arbitrage under model uncertainty. Finally we show that the term $K$ of finite-variance arising in the super-hedging strategy is interpreted as the max Profit\\&Loss of being short a delta-hedged option. The ask-bid spread is in fact the accumulation of summation of the superhedging $P\\&L$ and the subhedging $P\\&L $.
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中文摘要：
模型不确定性是一种不可避免的金融风险。定价模式选择上的错误可能会造成巨大的经济损失。本文研究了具有平均波动率不确定性的金融市常利用彭的G-随机演算建立了具有不确定先验分布的股票市场和期权市场模型。股票价格的过程用广义几何G-布朗运动来描述，其中平均不确定性可能与波动性不确定性一起移动，也可能与波动性不确定性无关。在套期保值市场上，根据Black-Scholes-Barenblatt方程推导出（奇异）期权的上限价格。有趣的是，相应的巴伦布拉特方程并不取决于投资者的风险偏好和标的股票的平均不确定性。因此，在适当的次线性预期下，投资者的风险偏好和标的股票的平均不确定性都不会对我们的超边缘和次边缘策略产生影响。对超级和次级套期保值策略给出了适当的套利定义，以使超级和次级套期保值价格合理。特别是次套期保值策略的套利条件填补了模型不确定性下套利理论的空白。最后，我们证明，超级对冲策略中产生的$K$有限方差被解释为做空增量对冲期权的最大损益。买卖价差实际上是超边际$P\\&L$和分边际$P\\&L$总和的累积。
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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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