Optimal lot sizing, process quality improvement and setup cost reduction
Operations Research
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Valuation of Investments in Real Assets with Implications for the Stock Prices
SIAM Journal on Control and Optimization
Real Options and Product Life Cycles
Management Science
Singular Stochastic Control, Linear Diffusions, and Optimal Stopping: A Class of Solvable Problems
SIAM Journal on Control and Optimization
OPTIMAL EXIT FROM A PROJECT WITH NOISY RETURNS
Probability in the Engineering and Informational Sciences
Investment Timing Under Incomplete Information
Mathematics of Operations Research
A Sequential Entry Problem with Forced Exits
Mathematics of Operations Research
Optimal Exit From A Deteriorating Project With Noisy Returns
Probability in the Engineering and Informational Sciences
A Numerical Method for Solving Singular Stochastic Control Problems
Operations Research
The Adoption of Multiple Dependent Technologies
Operations Research
Acquisition of Project-Specific Assets with Bayesian Updating
Operations Research
Risk Aversion, Indivisible Timing Options, and Gambling
Operations Research
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Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. To study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At each point in time, the firm can continue operations, or it can stop and exit the project. In addition, there is a one-time option to make an investment that boosts the project's profit rate. Using stochastic analysis, we show that the optimal policy always exists and that it is characterized by three thresholds. There are investment and exit thresholds before investment, and there is a threshold for exit after investment. We also effect a comparative statics analysis of the thresholds with respect to the drift and the volatility of the Brownian motion. When the profit boost upon investment is sufficiently large, we find a novel result: the investment threshold decreases in volatility.