Volume-Return portfolio selection and large scale dimensional problems with bivariate Markov chains

A portfolio selection problem is proposed under the assumption that financial returns follow homogenous Markovian chains. In this framework we describe two possible applications of bivariate Markov chains in portfolio selection problems. First, we show how to account the joint behavior of future wealth considering a bivariate Markov process and propose a technique to reduce the dimensionality of the large scale portfolio choice problem considering the heavy tails of the returns. Secondly, we describe the (volume, return) portfolio evolution with a bivariate Markov chain and we propose a volume-return portfolio strategy that accounts the investor behavior. Finally, we perform an ex-post analysis to assess the large-scale reduction technique used and the performance of a portfolio strategy that accounts the joint volume-return Markovian behaviour.