For radially symmetric μ, ν in d≥3 with α≠2, optimal stopping times maximizing/minimizing E[|B0−Bτ|^α] are unique non-randomized hitting times to symmetric barriers.
Optimal martingale transport between radially symmetric marginals in general dimensions
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abstract
We determine the optimal structure of couplings for the \emph{Martingale transport problem} between radially symmetric initial and terminal laws $\mu, \nu$ on $\R^d$ and show the uniqueness of optimizer. Here optimality means that such solutions will minimize the functional $\E |X-Y|^p$ where $0<p \leq 1$, and the dimension $d$ is arbitrary.
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math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Optimal Brownian stopping when the source and target are radially symmetric distributions
For radially symmetric μ, ν in d≥3 with α≠2, optimal stopping times maximizing/minimizing E[|B0−Bτ|^α] are unique non-randomized hitting times to symmetric barriers.