Bayesian Emulation for Multi-Step Optimization in Decision Problems

Abstract

We develop a Bayesian approach to computational solution of multi-step optimization problems, highlighted in the example of financial portfolio decisions. The approach involves mapping the technical structure of a decision analysis problem to that of Bayesian inference in a purely synthetic “emulating” statistical model. This provides access to standard posterior analytic, simulation and optimization methods that yield indirect solutions of the decision problem. We develop this in time series portfolio analysis using classes of economically and psychologically relevant multi-step ahead portfolio utility functions. Studies with multivariate currency time series illustrate the approach and show some of the practical utility and benefits of the Bayesian emulation methodology.