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We present a machine learning approach for finding minimal equivalentmartingale measures for markets simulators of tradable instruments, e.g. for aspot price and options written on the same underlying. We extend our results tomarkets with frictions, in which case we find "near-martingale measures" underwhich the prices of hedging instruments are martingales within their bid/askspread.  By removing the drift, we are then able to learn using Deep Hedging a "clean"hedge for an exotic payoff which is not polluted by the trading strategy tryingto make money from statistical arbitrage opportunities. We correspondinglyhighlight the robustness of this hedge vs estimation error of the originalmarket simulator. We discuss applications to two market simulators.

Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures