First passage times with Markov processes in porfolio selection problems
Institution: | Università degli studi di Bergamo |
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Department: | |
Year: | 2015 |
Keywords: | Markov Processes; Applied Probability; Portfolio Selection; Stopping times.; SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie |
Record ID: | 1223610 |
Full text PDF: | http://hdl.handle.net/10446/31899 |
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.