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 capitals to maximize the expected long-term growth rate of a utility function of the wealth. When the bond has a 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.
Bibliographical noteFunding Information:
The author is supported by NSF grant DMS-0904701, DARPA grant, and MacCracken Fellowship at New York University.
- 3/2 model
- Heston model
- Jump diffusion
- Long-term growth rate
- Optimal strategies
- Vasicek model