含摩擦情形下拟必然超对冲对偶性研究
数理金融
2019-09-19 v3
摘要
我们在模型不确定性下，证明了具有比例交易成本的离散时间金融市场的超对冲对偶性。摩擦通过偿付能力锥建模，如 [Kabanov, Y., Hedging and liquidation under transaction costs in currency markets. Fin. Stoch., 3(2):237-248, 1999] 的原始模型，并适配于 [Bouchard, B. and Nutz, M., Arbitrage and duality in nondominated discrete-time models. Ann. Appl. Probab., 25(2):823-859, 2015] 的拟必然框架。我们的方法消除了 [Bouchard, B., Deng, S. and Tan, X., Super-replication with proportional transaction cost under model uncertainty, Math. Fin., 29(3):837-860, 2019] 中所考虑的第二类无套利（No Arbitrage of the Second Kind）这一限制性假设，并在更自然的无严格套利（No Strict Arbitrage）条件下证明了对偶性。此外，我们将结果推广到具有组合约束的模型。
引用
@article{arxiv.1809.07516,
title = {On the quasi-sure superhedging duality with frictions},
author = {Erhan Bayraktar and Matteo Burzoni},
journal= {arXiv preprint arXiv:1809.07516},
year = {2019}
}
备注
Final version. To appear in Finance and Stochastics