We propose an iterated Azema-Yor type embedding in the spirit of Azema and Yor, 1979%DIFDELCMD < ] %%% and Brown et al., 2001%DIFDELCMD < ] %%% for any given finite number n of probability measures  which are in convex order and satisfy an additional technical assumption.  In particular, our construction reproduces the stopping boundaries obtained in Madan and Yor , 2002 and Brown et al. , 2001a%DIFDELCMD < ]%%% . We demonstrate with a counterexample that our technical assumption is necessary and propose an extended embedding for n=3. As a by-product of our analysis we compute the law of the maximum at all the stopping times. This is used in our parallel work Henry-Labordere et al. , 2013 to establish extremal properties of our embedding and develop robust pricing and hedging of Lookback options given prices of call options with multiple intermediate maturities .
We %DIFDELCMD < ] %%% %DIFDELCMD < ] %%% 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 %DIFDELCMD < ]%%% ). 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 .
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propose an iterated Azema-Yor type embedding in the spirit of
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given prices of call options with multiple intermediate maturities