In this paper we propose a formula to derive the value of a firm which is currently producing a certain product and faces the option to exit the market, whose demand follows a geometric Brownian motion. The problem of optimal exiting is an optimal stopping problem that can be solved using the dynamic programming principle. This is a free-boundary problem. We propose an approximation for the original model and, using the Implicit Function Theorem, we obtain the solution of the original problem. Finally we show, analytically, that the exit threshold is decreasing with the volatility as well as the drift of the geometric Brownian motion.

CEMAT - Center for Computational and Stochastic Mathematics