  The optimal strategies for a long-term static investor are studied. Given a
portfolio of a stock and a bond, we derive the optimal allocation of the
capitols to maximize the expected long-term growth rate of a utility function
of the wealth. When the bond has constant interest rate, three models for the
underlying stock price processes are studied: Heston model, 3/2 model and jump
diffusion model. We also study the optimal strategies for a portfolio in which
the stock price process follows a Black-Scholes model and the bond process has
a Vasicek interest rate that is correlated to the stock price.
