Quasiconvex analysis has important applications in several optimization problems in science and in particular in economics and finance, where convexity may be lost due to absence of global risk aversion, as for example in Prospect Theory. Quasiconvexity, i.e. the property ρ(λX + (1 − λ)Y ) ≤ max(ρ(X), ρ(Y )), plays also an important role in the theory or risk measures, since it enforce the control of the risk but it allows diversification. Moreover, the classical notion of the certainty equivalent, both in the static and in the dynamic formulations, is an example of a not convex but quasiconvex map. The robust or dual representation of convex maps plays a central role in the theory of risk measuring, especially for its connections with uncertainty and ambiguity. We provide a general dual representation of quasiconvex dynamic maps ρ : L(Ω, Ft, P) → L(Ω, Fs, P) and show its application in the above mentioned topics. This generalizes the representation of dynamic convex maps and of static (real valued) quasiconvex functions. Based on a joint paper with Marco Maggis, Milano University