Portfolio Selection and Risk Management with Markov Chains

This paper proposes markovian models in portfolio theory and risk management. At first, we describe discrete time optimal allocation models. Then, we examine the investor’s optimal choices either when the returns are uniquely determined by their mean and variance or when they are modeled by a Markov chain. We subject these models to back-testing on out-of-sample data, in order to assess their forecasting ability. Finally, we propose some models to compute VaR and CVaR when the returns are modeled by a Markov chain.