Dimension Reduction in Discrete Time Portfolio Optimization with Partial Information

This paper considers the problem of portfolio optimization in a market with partial information and discretely observed price processes. Partial information refers to the setting where assets have unobserved factors in the rate of return and the level of volatility. Standard filtering techniques are used to compute the posterior distribution of the hidden variables, but there is difficulty in finding the optimal portfolio because the dynamic programming problem is non-Markovian. However, fast time scale asymptotics can be exploited to obtain an approximate dynamic program (ADP) that is Markovian and is therefore much easier to compute. Of consideration is a model where the latent variables (also referred to as hidden states) have fast mean reversion to an invariant distribution that is parameterized by a Markov chain θt, where θt represents the regime-state of the market and reverts to its own invariant distribution over a much longer time scale. Data and numerical examples are also presented, and there appears to be evidence that unobserved drift results in an information premium