A Computational Method for Stochastic Impulse Control Problems

作者：Feng, Haolin^*; Muthuraman, Kumar

来源：Mathematics of Operations Research, 2010, 35(4): 830-850.

DOI：10.1287/moor.1100.0466

• impulse control
• free-boundary problem
• stochastic inventory control
• stochastic cash management

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 C(1), we show its optimality. We also provide an epsilon-optimality result. Finally, we illustrate a couple of popular applications of this model.

• 出版日期2010-11
• 单位中山大学