  For a long investment time horizon, it is preferable to rebalance the
portfolio weights at intermediate times. This necessitates a multi-period
market model in which portfolio optimization is usually done through dynamic
programming. However, this assumes a known distribution for the parameters of
the financial time series. We consider the situation where this distribution is
unknown and needs to be estimated from the data that is arriving dynamically.
We applied Bayesian filtering through dynamic linear models to sequentially
update the parameters. We considered uncertain investment lifetime to make the
model more adaptive to the market conditions. These updated parameters are put
into the dynamic mean-variance problem to arrive at optimal efficient
portfolios. Extensive simulations are conducted to study the effect of varying
underlying parameters and investment horizon on the performance of the method.
An implementation of this model to the S&P500 illustrates that the Bayesian
updating is strongly favored by the data and that it is practically
implementable.
