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Robust pricing and hedging under trading restrictions and the emergence of local martingale models

机译：交易限制下的稳健定价和对冲以及当地mar模型的出现

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摘要

We pursue the robust approach to pricing and hedging in which no probability measure is fixed, but call or put options with different maturities and strikes can be traded initially at their market prices. We allow the inclusion of robust modelling assumptions by specifying a set of feasible paths on which (super)hedging arguments are required to work. In a discrete-time setup with no short selling, we characterise absence of arbitrage and show that if call options are traded, then the usual pricing-hedging duality is preserved. In contrast, if only put options are traded, a duality gap may appear. Embedding the results into a continuous-time framework, we show that the duality gap may be interpreted as a financial bubble and link it to strict local martingales. This provides an intrinsic justification of strict local martingales as models for financial bubbles arising from a combination of trading restrictions and current market prices.
机译：我们采用稳健的定价和对冲方法，在这种方法中，没有固定概率度量，但是具有不同到期日和行使价的看涨期权或看跌期权可以首先以其市场价格进行交易。通过指定一组（超级）对冲参数必须起作用的可行路径，我们允许包含鲁棒的建模假设。在没有卖空的离散时间设置中，我们描述了没有套利的特征，并表明，如果看涨期权被交易，则通常的定价套期保值对偶得以保留。相反，如果只买卖看跌期权，则可能会出现双重性缺口。将结果嵌入到连续时间框架中，我们证明了双重性鸿沟可能被解释为金融泡沫，并将其与严格的当地link市场联系起来。这提供了严格的本地mar鱼的内在理由，将其作为贸易限制和当前市场价格相结合而产生的金融泡沫的模型。

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