A large debate is open for several years within mathematical nance about the criterion to optimise, in particular for long term policy. From the perspective of public decision, such strategy must be time consistent. Moreover the use of adaptative criterion is necessary to integrate some major variation in the environment. A typical example is the forward utilities introduced by M. Musiela and T. Zariphopoulou in 2003, for which there is no-prespecied trading horizon. First we characterize utility random elds by showing that the associated marginal utility is a monotonic solution of SDE with random coecients; its inverse, the marginal conjuguate utility is solution of a SPDE driven by the adjoint elliptic operator. When forward utilities satisfy a property of consistency with a given incomplete nancial market, as in the classical case, dynamic utilities and its conjugate may be characterized in terms of Hamilton Jacobi Bellman SPEs as value functions of control problems. More interesting is the splitting property of the marginal utility in terms of optimal processes, leading to an explicit solution given by the composition of the optimal conjugate process with the inverse of the optimal wealth. Then, it is possible to generate time consistency yield curves by indif- ference pricing. In the controversy on the discount rate used in nancing long term projects, such a criterion leads to a time consistency yield curve depending of the wealth of the economy.