Optimal Portfolio and Consumption with Transaction Costs

In Chapter 1, we study optimal portfolio and consumption with both fixed and proportional transaction costs. For a power utility function we find an explicit solution to the HJB equation governing the no-transaction region. Based on the explicit solution, we formulate a combined stochastic and impulse control problem as a quasi-variational inequality and find the transaction regions, the no-transaction region, and the boundary curves separating them. We show that the explicit solution we find satisfies the verification theorem and it is also a viscosity solution for the quasi-variational inequality. We present numerical results where we compare the various cases of the fixed and proportional transaction costs.;In Chapter 2, we discuss the optimal portfolio and consumption on multiple risky assets with both fixed and proportional transaction costs. Explicit solutions to the corresponding HJB equations are provided. The explicit solutions are viscosity solutions. Numerical results for two risky assets and N risky assets are given.