In this thesis, we discuss the optimal liquidation problem in a finite horizon model with
permanent and temporary pricing impact. We use different model set-ups including a finite time Markov diffusion model and a regime switching model with exit time. The drift
and diffusion terms of the asset price are general functions depending on the state variables as well as the control. There is also a non-linear transaction cost associated with the
liquidation. We verify the continuity of the value function and show that it is the unique
viscosity solution of the associated HJB equation. We also propose a perturbation method
to approximate the viscosity solution through a series of classical solutions with the help of
the stability property of viscosity solutions. We revise the definition of viscosity solutions
for the regime switching model and show that the value function is a strong-form viscosity
solution. Numerical results are presented at the end to show the relationship between the
optimal selling rate and the state variables.