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.
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 densities with regard to Kullback-Leibler risk and, under certain conditions, quadratic risk.