英文标题：
《Robust pricing and hedging under trading restrictions and the emergence
of local martingale models》
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作者：
Alexander M.G. Cox, Zhaoxu Hou and Jan Obloj
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最新提交年份：
2015
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英文摘要：
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options are traded at certain maturities, and the forward price implied by these option prices may be strictly decreasing in time. In discrete time, when call options are traded, the short-selling restrictions ensure no arbitrage, and we show that classical duality holds between the smallest super-replication price and the supremum over expectations of the payoff over all supermartingale measures. More surprisingly in the case where the only vanilla options are put options, we show that there is a duality gap. Embedding the discrete time model into a continuous time setup, we make a connection with (strict) local-martingale models, and derive framework and results often seen in the literature on financial bubbles. This connection suggests a certain natural interpretation of many existing results in the literature on financial bubbles.
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中文摘要：
我们考虑在有交易限制的情况下，在离散和连续时间内，衍生工具的定价，但不对基础模型进行任何概率假设。特别是，我们假设欧洲看跌期权或看涨期权在某些到期日进行交易，这些期权价格隐含的远期价格可能会随着时间的推移而严格下降。在离散时间内，当看涨期权交易时，卖空限制确保没有套利，我们证明了经典对偶性在最小超复制价格和所有超鞅测度下的收益预期的上确界之间成立。更令人惊讶的是，在唯一的普通期权是看跌期权的情况下，我们证明了存在二元性缺口。将离散时间模型嵌入到连续时间系统中，我们与（严格的）局部鞅模型建立了联系，得到了金融泡沫文献中常见的框架和结果。这种联系表明，对金融泡沫文献中的许多现有结果有某种自然的解释。
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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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