投资组合约束下的模型无关超套期保值
Model-independent Superhedging under Portfolio Constraints
摘要：
在离散时间市场中，我们研究了模型独立的超套期保值，而半静态的超套期保值投资组合由{ \it three}部分组成：在流动性交易的香草呼叫的静态位置，在其他可交易的静态位置，但可能流动性较低，异国情调的选择，并在一定的限制下，在风险资产的动态交易策略。通过考虑每个可交易的奇异期权的限价订单簿，利用Monge-Kantorovich最优运输理论，建立了一般的超套期保值对偶，它与凸风险测度有着天然的联系.借助于这种对偶性，我们导出了资产定价基本定理的一个与模型无关的版本。引入了弱于无套利的“有限最优套利利润”概念。值得注意的是，我们的方法涵盖了一大类Delta约束以及Gamma约束。
英文摘要：
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading strategy in risky assets under certain constraints. By considering the limit order book of each tradable exotic option and employing the Monge-Kantorovich theory of optimal transport, we establish a general superhedging duality, which admits a natural connection to convex risk measures. With the aid of this duality, we derive a model-independent version of the fundamental theorem of asset pricing. The notion "finite optimal arbitrage profit", weaker than no-arbitrage, is also introduced. It is worth noting that our method covers a large class of Delta constraints as well as Gamma constraint.
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