First passage times with Markov processes in porfolio selection problems

This thesis analyses the impact of parametric timing portfolio strategies on the U.S. stock market. In particular, we assume that the log-returns follow a given parametric Lévy process and we describe a methodology to approximate the distributions of stopping times using the underlying Markov transition matrix. We extend the analysis to non-Lévy processes, considering Markov Regime switching model and the log-Student-t model. Therefore, we propose the use of portfolio strategies based on the maximization of the ratio between the expected first passage time to reach a low level of wealth and the expected first passage time to reach a high level of wealth. Finally, we compare the ex-post wealth obtained maximizing the ratio of proper expected stopping times under different distributional assumptions.