In the present paper, we are interested in the forward-looking inverse problem, where the observable are a so-called characteristic process $X^c$ and an initial utility function $U (0, .) = u(.)$. The recovery process is a dynamic (eventually random) utility performance $U$. The main result is a necessary and sufficient condition for the existence of a utility performance process $U$ satisfying $U (t, X^c_t (x))$ is a martingale for any initial starting point $x$. Examples of applications are developed in the last section to support our approach in the special case of finance and economics: the first example concerns an aggregation problem, the second one a Markov equilibrium.