Before revision:  We develop a novel strategy based on stochastic processes, where the predictive processes are expressed as stochastic differential equations, evaluated using It\^{o show that a specific form of non-linear BPS (as in McAlinn and West, 2019) produces exact minimax predictive distributions for Kullback-Leibler risk and, under certain conditions, quadratic risk. A finite sample simulation study is presented to illustrate our results .
After revision:  We develop a novel strategy based on stochastic processes, where the predictive processes are expressed as stochastic differential equations, evaluated using It\^{o show that a specific form of non-linear BPS (as in McAlinn and West, 2019) produces exact minimax predictive distributions for Kullback-Leibler loss, providing theoretical support for finite sample predictive performance over existing ensemble methods. A simulation study that highlights this theoretical result is presented, showing that dynamic Bayesian predictive synthesis is superior to other ensemble methods using multiple metrics .