金融市场的稳健套利条件
Robust Arbitrage Conditions for Financial Markets
摘要：
本文以Wasserstein距离为模糊性测度，研究了分布不确定性下金融市场的套利性质。考虑了经典套利条件的弱形式和强形式。引入了一个松弛，为此我们创造了术语统计套利。得到了鲁棒套利条件的简单对偶形式。在这方面出现了一些有趣的问题。一个问题是：我们能否计算出一个临界沃瑟斯坦半径，超过这个半径就存在套利机会？将模糊程度映射到统计套利水平的曲线是什么形状？其他问题出现的最佳（最坏）情况分布和最优投资组合的结构。为了回答这些问题，一些理论的发展和计算实验进行了具体的问题实例。最后，本文提出了一些有待解决的问题和对未来研究的建议。
英文摘要：
This paper investigates arbitrage properties of financial markets under distributional uncertainty using Wasserstein distance as the ambiguity measure. The weak and strong forms of the classical arbitrage conditions are considered. A relaxation is introduced for which we coin the term statistical arbitrage. The simpler dual formulations of the robust arbitrage conditions are derived. A number of interesting questions arise in this context. One question is: can we compute a critical Wasserstein radius beyond which an arbitrage opportunity exists? What is the shape of the curve mapping the degree of ambiguity to statistical arbitrage levels? Other questions arise regarding the structure of best (worst) case distributions and optimal portfolios. Towards answering these questions, some theory is developed and computational experiments are conducted for specific problem instances. Finally some open questions and suggestions for future research are discussed.
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