Article ID: | iaor20108770 |
Volume: | 35 |
Issue: | 4 |
Start Page Number: | 830 |
End Page Number: | 850 |
Publication Date: | Nov 2010 |
Journal: | Mathematics of Operations Research |
Authors: | Muthuraman Kumar, Feng Haolin |
We consider the instantaneous control of a diffusion process on the real line. Two types of costs are incurred. The holding cost rate, incurred at all times, is modeled by a convex function. Transactions costs have both fixed and proportional components, making it an impulse control problem. The objective is to minimize the expected infinite horizon discounted cost. The solution to a quasi-variational inequality, which takes the form of a free-boundary problem, can be shown to be the optimal solution. We develop a methodology that converts the free-boundary problem into a sequence of fixed boundary problems. We show that the arising sequence is monotonic and converges. Provided the converged solution is