| Abstract: |
| A portfolio optimization problem of the Merton`s type with complete memory (infinite delay) over a finite time horizon is considered. In this model, the volatility of risky asset is considered to be stochastic. The goal is to choose the optimal investment and consumption controls to maximize the investor`s expected total discounted utility. Using dynamic programming principle, the Hamilton-Jacobi-Bellman (HJB) equation is derived. Then, using the subsolution/supersolution method, we establish the existence result of classical solution to the HJB equation. Finally, we verify that the solution is equal to the value function, and derive the optimal investment and consumption controls. |
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