| Abstract: |
| This work extends the portfolio optimization problem via utility maximization in the presence of proportional transaction costs to regime-switching models. With regime-switching, the Hamilton-Jacobi-Bellman (HJB) equation becomes a system of $m_0$ coupled variational equalities where $m_0$ is the total number of regimes considered for the market. We consider a power utility function and establish important properties of the value function including the continuity in both time and state variables and the unique viscosity solution of the HJB equation. A numerical procedure is developed based on the formulation of the optimization in discrete time, and using an efficient discrete tree approximation of the underlying continuous time process. |
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