Some examples of Skorokhod embeddings obtained from the Azéma–Yor algorithm

As discussed in Madan and Yor (2002) [10], under certain conditions on a family ( H r , r > 0 ) of Hardy–Littlewood functions, Markovian Martingales ( B T H r ) may be constructed. We take advantage of the explicit character of the Azéma–Yor (Skorokhod embedding) algorithm, to describe precisely some remarkable and simple examples of these Markovian Martingales.