Abstract
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Several applications are provided: martingale measures with volatility uncertainty, optimal transport with capacity constraints, and Skorokhod embedding with bounded times. Next, we extend this result to multi-marginal constraints. Finally, we consider an optimal transport problem with constraints and obtain its Kantorovich duality. A corollary of this result is a monotonicity principle which gives a geometric way of identifying the optimizer.
Original language | English (US) |
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Pages (from-to) | 1131-1158 |
Number of pages | 28 |
Journal | Applied Mathematics and Optimization |
Volume | 84 |
Issue number | 1 |
DOIs | |
State | Published - Aug 2021 |
Keywords
- Bounded volatility/quadratic variation
- Domain constraints
- G-expectations
- Kantorovich duality
- Martingale optimal transport
- Monotonicity principle
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics