  We investigate the performance of the Deep Hedging framework under training
paths beyond the (finite dimensional) Markovian setup. In particular we analyse
the hedging performance of the original architecture under rough volatility
models with view to existing theoretical results for those. Furthermore, we
suggest parsimonious but suitable network architectures capable of capturing
the non-Markoviantity of time-series. Secondly, we analyse the hedging
behaviour in these models in terms of P\&L distributions and draw comparisons
to jump diffusion models if the the rebalancing frequency is realistically
small.
