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When terminal facelift enforces delta constraints

机译：当终端改造强制实施增量约束时

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This paper deals with the superreplication of non-path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding superreplication price of a given claim has been widely studied in the literature, and its terminal value, which dominates the claim of interest, is the so-called facelift transform of the claim. We investigate under which conditions the superreplication price and strategy of a large class of claims coincide with the exact replication price and strategy of the facelift transform of this claim. In one dimension, we observe that this property is satisfied for any local volatility model. In any dimension, we exhibit an analytical necessary and sufficient condition for this property, which combines the dynamics of the stock together with the characteristics of the closed convex set of constraints. To obtain this condition, we introduce the notion of first order viability property for linear parabolic PDEs. We investigate in detail several practical cases of interest: multidimensional Black-Scholes model, non-tradable assets, and short-selling restrictions.
机译：本文讨论了在投资组合中所持股份数量受到额外凸约束的情况下，非路径依赖的欧洲债权的超额复制。给定索赔的相应超级复制价格已在文献中进行了广泛研究，其终值主导着利息索赔，即所谓索赔的换装变换。我们调查在哪种条件下，一大类索赔的超级复制价格和策略与该索赔的整容转换的确切复制价格和策略一致。在一个维度上，我们观察到任何局部波动率模型都满足该属性。在任何维度上，我们都显示出对此属性进行分析的必要条件和充分条件，该条件将股票的动力学与封闭凸集约束的特征结合在一起。为了获得这种条件，我们引入了线性抛物线偏微分方程的一阶生存能力的概念。我们将详细研究一些感兴趣的实际案例：多维Black-Scholes模型，不可交易资产和卖空限制。

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