Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Optimal Exit From A Deteriorating Project With Noisy Returns
Probability in the Engineering and Informational Sciences
Invest or Exit? Optimal Decisions in the Face of a Declining Profit Stream
Operations Research
Acquisition of Project-Specific Assets with Bayesian Updating
Operations Research
Optimal markdown pricing strategy with demand learning
Probability in the Engineering and Informational Sciences
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We consider the problem of selecting a stopping time &tgr; 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 &mgr; and variance σ2. The profit rate &mgr; never changes over time, but &mgr; is not directly observable. Specifically, &mgr; takes the value &mgr;H 0 when in the high state and &mgr;L p0 that the project is in the high state is known. The decision-maker seeks to maximize the expected discounted profit up to time &tgr;. 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 |&mgr;L|, provided |&mgr;L| is large.