Nhat Thu Tran

• This thesis focuses on dealing with some new aspects of continuous time portfolio optimization by using the stochastic control method. First, we extend the Busch-Korn-Seifried model for a large investor by using the Vasicek model for the short rate, and that problem is solved explicitly for two types of intensity functions. Next, we justify the existence of the constant proportion portfolio insurance (CPPI) strategy in a framework containing a stochastic short rate and a Markov switching parameter. The effect of Vasicek short rate on the CPPI strategy has been studied by Horsky (2012). This part of the thesis extends his research by including a Markov switching parameter, and the generalization is based on the B\"{a}uerle-Rieder investment problem. The explicit solutions are obtained for the portfolio problem without the Money Market Account as well as the portfolio problem with the Money Market Account. Finally, we apply the method used in Busch-Korn-Seifried investment problem to explicitly solve the portfolio optimization with a stochastic benchmark.