Teissier's problem on proportionality of nef and big classes over a compact K\"ahler manifold

We solve Teissier's proportionality problem for transcendental nef classes over a compact K\"ahler manifold which says that the equality in the Khovanskii-Teissier inequalities hold for two nef and big classes if and only if the two classes are proportional. This result recovers the previous one of Boucksom-Favre-Jonsson for the case of nef and big line bundles over a (complex) projective algebraic manifold.