The Azéma-Yor Embedding in Brownian Motion with Drift

x e 2 t dF (t) (x2 IR) and we set h (s) = 1 for s C . This settles the question raised in [6]. In addition, it is proved that is pointwise the smallest possible stopping time satisfying (B + ) which generates stochastically the largest possible maximum of the process (Bt+ t)t 0 up to the time of stopping. This minimax property characterizes uniquely. The result recovers the Azéma-Yor solution of the Skorokhod embedding problem [1] by passing to the limit when # 0 . The condition on the existence of a strictly positive density is imposed for simplicity, and more general cases can be treated similarly. The line of arguments used in the proof can be extended to treat the case of more general nonrecurrent diffusions.