  We solve the $n$-marginal Skorokhod embedding problem for a continuous local
martingale and a sequence of probability measures $\mu_1,...,\mu_n$ which are
in convex order and satisfy an additional technical assumption. Our
construction is explicit and is a multiple marginal generalisation of the Azema
and Yor (1979) solution. In particular, we recover the stopping boundaries
obtained by Brown et al. (2001) and Madan and Yor (2002). Our technical
assumption is necessary for the explicit embedding, as demonstrated with a
counterexample. We discuss extensions to the general case giving details when
$n=3$.
  In our analysis we compute the law of the maximum at each of the n stopping
times. This is used in Henry-Labordere et al. (2013) to show that the
construction maximises the distribution of the maximum among all solutions to
the $n$-marginal Skorokhod embedding problem. The result has direct
implications for robust pricing and hedging of Lookback options.
