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.
Ob/suppress l´ oj, The Skorokhod embedding problem and its offspring Probability Surveys, 1 (2004) 321–392
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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.