{"ID":2858151,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08182","arxiv_id":"2510.08182","title":"Frictional martingale optimal transport and robust hedging","abstract":"We study the martingale optimal transport problem with state-dependent trading frictions and develop a geometric and duality framework extending from the one time-step to the multi-marginal setting. Building on the left-monotone structure of frictionless MOT (Beiglböck and Juillet, Ann. Probab., 2016; Henry-Labordère and Touzi, Finance Stoch., 2016; Beiglböck et al., Ann. Probab., 2017), we introduce a convex frictional cost combining proportional bid-ask spreads and quadratic liquidity impacts. The framework extends the martingale Spence-Mirrlees condition to nonlinear frictions and establishes a frictional monotonicity principle. At each time step, the joint distribution between consecutive asset prices exhibits a bi-atomic, monotone geometry: conditional on the current price, the next price lies on one of two monotone branches representing upward and downward rebalancing. A no-transaction region, or trade band, arises where maintaining the position is optimal, while outside the band, transitions follow two monotone graphs whose endpoints satisfy an equal-slope condition balancing continuation value and marginal trading cost. The framework extends dynamically via a recursive identity, ensuring stability and convergence to the frictionless left-curtain limit, and applies to model-independent pricing and robust hedging of path-dependent derivatives.","short_abstract":"We study the martingale optimal transport problem with state-dependent trading frictions and develop a geometric and duality framework extending from the one time-step to the multi-marginal setting. Building on the left-monotone structure of frictionless MOT (Beiglböck and Juillet, Ann. Probab., 2016; Henry-Labordère a...","url_abs":"https://arxiv.org/abs/2510.08182","url_pdf":"https://arxiv.org/pdf/2510.08182v2","authors":"[\"Pratik Rai\"]","published":"2025-10-09T13:07:37Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.FA\",\"math.PR\"]","methods":"[]","has_code":false}