Parameter uncertainty and learning in dynamic financial decisions

When the asset allocation problem is implemented using historical data, parameter uncertainty can degrade the desirable properties of the optimal portfolio strategy. Given the uncertainty in parameters and given that investors learn by observation, it is natural to formulate asset allocation problems using a Bayesian framework. The most relevant literature on Bayesian portfolio analysis is reviewed. The multi-period Bayesian asset allocation problem is formulated, and the necessary conditions for learning in discrete time are established. The Bayesian learning process is discussed for various linear conditionally normal models. For these models, the learning process is shown to be a Bayesian version of the well-known Kalman filter. A regime-switching model is discussed, and the learning process for the unobserved regime is derived using Bayesian analysis. It is shown that for all models considered, the learning process constitutes a compact filter on observations and therefore allows a Markovian representation of dynamic multi-period allocation problems in discrete time, which is a necessary condition for the problem to remain solvable.