American and European Portfolio Selection Strategies: the Markovian Approach

In this chapter we propose portfolio selection strategies using the assumption that the portfolio returns evolve as Markov processes. In particular, we distinguish the analysis for parametric and non parametric Markov processes and discuss the construction of the transition matrix in the two different cases. Under the assumption that returns are Markov processes we propose several possible strategies where the investors recalibrate their portfolios at a fixed temporal horizon or within a fixed temporal horizon. Thus, we analyze the computational complexity of the proposed strategies and propose an heuristic algorithm for the global optimum in order to overcome the intrinsic computational complexity of the proposed models. Furthermore, we show how the Markov assumption can be used to forecast the portfolio returns and we examine some simple empirical comparisons between Markovian strategies and classic reward-risk ones.