Horikawa and Nakagawa (2024) claim that in a complete market admitting statistical arbitrage, the difference between the deep hedging and the replicating portfolio hedging positions is a statistical arbitrage. Deep hedging can thus include an undesirable speculative component. We test whether this remains true in a GARCH-based incomplete market dynamics. We observe that the difference between deep hedging and delta hedging is a speculative overlay if the risk measure considered does not put sufficient relative weight on adverse outcomes. Nevertheless, a suitable choice of risk measure can prevent the deep hedging agent from engaging in speculation.

中文翻译：

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深度对冲和 delta 对冲之间的区别是统计套利吗？


Horikawa 和 Nakagawa （2024） 声称，在接受统计套利的完整市场中，深度对冲和复制投资组合对冲头寸之间的差异是统计套利。因此，深度对冲可以包含不良的投机成分。我们测试了在基于 GARCH 的不完整市场动态中是否仍然如此。我们观察到，如果所考虑的风险指标没有对不良结果给予足够的相对权重，那么深度对冲和 delta 对冲之间的差异是一种投机性叠加。尽管如此，选择合适的风险措施可以防止深度对冲代理进行投机。