Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price ansatz for maximizing long-term returns, given average volatility yields a strategy that is, for small bid–ask spreads, asymptotically optimal at the third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at the fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices.

中文翻译：

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几乎完美的影子价格

影子价格通过将优化转移到更容易处理、无摩擦的市场，简化了具有交易成本的市场中最优交易策略的推导。本文建立了一个用于最大化长期回报的朴素影子价格模拟，在给定平均波动性的情况下，产生了一种策略，即对于较小的买卖差价，在三阶上渐近最优。考虑到交易成本的二阶影响，这样的策略本质上是最优的。然而，对于与另一种不同的风险规避，我们设计了优于第四阶影子市场的替代策略。最后，结果表明风险中性目标排除了影子价格的存在。