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Deep Learning Algorithms for Hedging with Frictions

Xiaofei ShiDaran XuZhanhao Zhang
摘要
This work studies the optimal hedging problems in frictional markets withgeneral convex transaction costs on the trading rates. We show that, under thesmallness assumption on the magnitude of the transaction costs, the leadingorder approximation of the optimal trading speed can be identified through thesolution to a nonlinear SDE. Unfortunately, models with arbitrary statedynamics generally lead to a nonlinear forward-backward SDE system, wherewellposedness results are unavailable. However, we can numerically find theoptimal trading strategy with the modern development of deep learningalgorithms. Among various deep learning structures, the most popular choicesare the FBSDE solver introduced in the spirit by [32] and the deep hedgingalgorithm pioneered by [12, 14, 15, 16, 35, 36, 45, 47]. We implement thesedeep learning algorithms with calibrated parameters from [26] and compare thenumerical results with the leading order approximations. This work documentsthe performance of different learning-based algorithms and provides betterunderstandings of their advantages and drawbacks.
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