Entry–Exit Decisions with Underlying Processes Following Geometric Lévy Processes

Abstract

We study, from the perspective of optimal stopping theory, entry–exit decision problems of a project in the context that the log-price process follows a Lévy process with exponential jumps. A closed-form solution to the problems is obtained. To be specific, we show explicitly an optimal entry time, an optimal exit time and an expression of the maximal expected present value of the project. Moreover, it is also anatomized how the jumping of the Lévy process affects optimal entry and exit times. While the negative effect of jumping on prices grows, the optimal exit time gets earlier, and the optimal entry time, however, first moves up and then moves down. In addition, the optimal exit time decreases with the frequency increasing of jumps when the negative effect dominates the positive effect, and increases when the opposite situation holds; the optimal entry time first increases and then decreases as the frequency becomes higher if the negative effect dominates the positive effect, and increases if the contrary condition is satisfied.