Abstracts

I analyze the optimal allocation of wealth to cash, bonds, and stocks when the interest rate is stochastic and the stock index has a time-varying mean. I find that, under certain economic conditions, the investor may optimally increase investments in stocks and bonds at the same time, which is due to the dynamic trading policies and the correlation between the asset classes. I also find that in different economic regimes, short-term investors have very different investment policies than long-term investors. Thus, dynamic asset allocation with nonzero bond-stock correlation helps explain why, during extreme market conditions such as the recent financial crisis, some investors sold all types of assets short, whereas other investors considered it an unprecedented buying opportunity. In order to avoid the dimensionality problem of the partial differential equation that corresponds to the framework I use, I will apply a method that is similar to former results in the literature, see for example Zariphopolou (1999, Mathematical Methods for Operations Research) and Benth and Karlsen (2001, International Journal of Applied and Theoretical Finance), but is slightly more complex, as I consider a portfolio of both cash, bonds, and stocks with a nonzero correlation structure. Despite this, I give an analytical solution to the indirect utility function as well as the optimal trading policy, proved via a verification theorem.