Optimal investment problem under non-extensive statistical mechanics

The optimal investment problem in which the asset price process is modeled by the non-extensive statistical mechanics is studied in this paper. By the methods of deterministic control and the dynamic programming, we obtain the optimal strategy with logarithmic utility function, power utility function and quadratic utility function, respectively. Moreover, the numerical results indicate that the optimal investment strategy is affected by the non-extensive parameter, the proportion invested in the risky asset decreases as the wealth increases under quadratic utility function, but it remains unchanged under power utility and logarithmic utility function.