OPTIMAL EXIT FROM A PROJECT WITH NOISY RETURNS

Abstract

We consider the problem of selecting a stopping time τ which determines when to exit an investment project when the project's cumulative profit up to time t is Xt, where {Xt : t ≥ 0} is a Brownian motion with drift μ and variance σ2. The profit rate μ never changes over time, but μ is not directly observable. Specifically, μ takes the value μH > 0 when in the high state and μL < 0 when in the low state, and the initial probability p0 that the project is in the high state is known. The decision-maker seeks to maximize the expected discounted profit up to time τ. Using the theory of stochastic differential equations, we show that it is optimal to exit only when the posterior probability Pt of being in the high state falls below a critical number p*, and we produce a simple, closed form for p*. Our most surprising comparative-statics result is that the expected discounted profit increases with |μL|, provided |μL| is large.

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