  The recent work of Horikawa and Nakagawa (2024) claims that under a complete
market admitting statistical arbitrage, the difference between the hedging
position provided by deep hedging and that of the replicating portfolio is a
statistical arbitrage. This raises concerns as it entails that deep hedging can
include a speculative component aimed simply at exploiting the structure of the
risk measure guiding the hedging optimisation problem. We test whether such
finding remains true in a GARCH-based market model. We observe that the
difference between deep hedging and delta hedging can be a statistical
arbitrage 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 including a speculative overlay within its
hedging strategy.
