论影子价格的存在
On the Existence of Shadow Prices
摘要：
对于比例交易成本下的效用最大化问题，人们已经观察到，具有交易成本的原始市场有时可以被无摩擦的“影子市场”所取代，该影子市场产生相同的最优策略和效用。然而，到目前为止，这是否确实普遍适用的问题仍然难以捉摸。在本文中，我们提出了一个反例，表明影子价格可能不存在。另一方面，我们证明了卖空约束是保证其存在的充分条件，即使在非常一般的多货币市场模型可能不连续的买卖价差。
英文摘要：
For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless "shadow market" that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper we present a counterexample which shows that shadow prices may fail to exist. On the other hand, we prove that short selling constraints are a sufficient condition to warrant their existence, even in very general multi-currency market models with possibly discontinuous bid-ask-spreads.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
