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A Sequential Entry Problem with Forced Exits

Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
huiwang{at}cfm.brown.edu

We consider a continuous time optimal stopping problem with multiple entries and forced exits. The value for such an optimization problem with a general payoff function is solved in closed form under the assumption that the state process is a geometric Brownian motion and the forced exits come in according to a Poisson process. The effect due to the forced exits is analyzed. It is shown that the presence of the forced exits is a true risk (meaning that it will reduce the value and enlarge the "continuation" region) if and only if the entry cost is large enough compared to the running cost.

Key Words: optimal stopping; forced exits; variational inequality
History: Received: July 16, 2003; revision received: June 3, 2004;revision received: September 7, 2004;