Economic applications of regulated Brownian motion
This work presents three models of risk-neutral optimizing firms that are faced with an uncertain environment modelled as a continuous shock following a geometric Brownian motion, and some type of market imperfection that induces costs when the firms change their choice variables. One model presents a firm deciding its investment policy when there are fixed transactions costs and a spread between the purchase and resale price of capital. Another presents a firm that produces in one country and sells in another. It faces a random exchange rate and menu costs. The choice variable is the foreign price charged. Finally an inventory model is studied with standard holding and adjustment costs. To maintain homogeneity, the shocks are also assumed to follow a geometric Brownian motion process. The solutions are characterized by two regions, a region of inaction where firms do not find it in their interest to change the choice variable because the costs of doing so outweigh the benefits. In the other region firms find it always optimal to change the choice variable because benefits outweigh costs. Solutions are obtained using regulated Brownian motion techniques that imply the solution of a standard Hamilton-Jacobi-Bellman equation and the imposition of what is referred to as smooth fit at the boundaries of the region of no action. Standard comparative dynamic exercises produce increases in the parameters of market imperfection or uncertainty induce an increase in the area of inaction.
Delgado, Francisco Antenor, "Economic applications of regulated Brownian motion" (1990). Dissertations available from ProQuest. AAI9026543.