Before revision:   In particular, we construct AY martingales with a given terminal law and this allows us to rediscover the AY solution to the Skorokhod embedding problem.
After revision:  We establish relations between Average Value at Risk, Drawdown function, Hardy-Littlewood transform and its generalised inverse. In particular, we construct AY martingales with a given terminal law and this allows us to rediscover the AY solution to the Skorokhod embedding problem.