Bayesian learning in dynamic portfolio selection under a minimax rule

We are concerned about a multi-period portfolio selection problem where the issue of parameter uncertainty for the distribution of risky asset returns should be addressed properly. For analysis, we first propose a novel dynamic portfolio selection model with an $$l_{\infty }$$ l ∞ risk function, instead of the classic portfolio variance, used as risk measure. The investor in our model is assumed to choose the optimal portfolio by maximizing the expected terminal wealth at a minimum level of cumulative risk, quantified by a weighted sum of the risks in subsequent periods. The proposed multi-period model has a closed-form optimal policy that can be constructed and interpreted intuitively. We introduce Bayesian learning to account for the uncertainty in estimates of unknown parameters and discuss the impact of Bayesian learning on the investor’s decision making. Under an i.i.d. normal return-generating process with unknown means and covariance matrix, we show how Bayesian learning promotes diversification and reduces sensitivity of optimal portfolios to changes in model inputs. The numerical results based on real market data further support that the model with Bayesian learning can perform much better than a plug-in model out-of-sample with the extent of performance improvement affected by the investor’s level of risk aversion and the amount of data available.