| Abstract: |
| We consider an optimal portfolio problem where the underlying risky assets are driven by the factor model with delay feature in order to describe the short term forecasting and the interaction with time delay among different financial markets. The delay phenomenon can be recognized as the integral type and the pointwise type. The optimal strategy is identified by maximizing the power utility. Due to the delay leading to the non-Markovian structure, the conventional PDE approaches are no longer applicable. Instead of using dynamic programming, we obtain the optimal strategy can be characterized by the solutions of a quadratic forward backward stochastic dierential equations(QFBSDEs). The optimality is verified via the super-martingale argument. The existence and uniqueness of the solution to the QFBSDEs are established without requiring the assumption of complete market. In addition, we analyze three particular cases where the corresponding FBSDEs can be solved explicitly.
The discussion is based on a joint work with Li-Hsien Sun and Zheng Zhang. |
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