Optimal Stopping of Stochastic Transport Minimizing Submartingale Costs

13 Mar 2020 Ghoussoub Nassif Kim Young-Heon Palmer Aaron Zeff

Given a stochastic state process $(X_t)_t$ and a real-valued submartingale cost process $(S_t)_t$, we characterize optimal stopping times $\tau$ that minimize the expectation of $S_\tau$ while realizing given initial and target distributions $\mu$ and $\nu$, i.e., $X_0\sim \mu$ and $X_\tau \sim \nu$. A dual optimization problem is considered and shown to be attained under suitable conditions... (read more)

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