DOES THE CHOICE OF RISK MEASURE DETERMINE HEDGING ROBUSTNESS? EVIDENCE FROM DEEP REINFORCEMENT LEARNING IN FX MARKETS

This paper formulates the delta hedging problem for FX options as a stochastic optimal control problem and solves it via deep reinforcement learning. Four neural policy specifications, differing in their risk measure objective (MSE, mean-variance, and two CVaR variants), are trained on synthetic BRL/USD trajectories generated by a Wasserstein GAN with Gradient Penalty. The policies are benchmarked against the analytical Garman-Kohlhagen delta across 75 experimental configurations spanning three time horizons, five moneyness levels, and five transaction cost structures, stratified across five market regimes identified via Dynamic Time Warping clustering. Three of the four neural policies reduce out-of-sample MSE by 76% to 85%. The mean-variance specification achieves the lowest MSE overall, while the unregularized MSE specification exhibits catastrophic instability with variance 27 times higher.