As the main technical tool in solving the generalized Kyle-Back insider trading models in which the insider can use dynamic information,  we study a class of Stochastic Two-Point Boundary Value Problems (STPBVP), which resembles the dynamic Markov bridge in the literature without insisting on its local martingale requirement. In the case when the solution of the STPBVP has an affine structure, we show that the Kyle-Back equilibrium can be determined by the decoupling field of a special forward-backward SDE obtained via a non-linear filtering argument, along with a set of compatibility conditions.