Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/59672 
Year of Publication: 
2009
Series/Report no.: 
Discussion Paper No. 1480
Publisher: 
Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, Evanston, IL
Abstract: 
This paper establishes that the optimal stopping time of virtually any optimal stopping problem is increasing in patience, understood as a particular partial order on discount rate functions. With Markov dynamics, the result holds in a continuation- domain sense even if stopping is combined with an optimal control problem. Under intuitive additional assumptions, we obtain comparative statics on both the optimal control and optimal stopping time for one-dimensional diffusions. We provide a simple example where, without these assumptions, increased patience can precipitate stopping. We also show that, with optimal stopping and control, a project's expected value is decreasing in the interest rate, generalizing analogous results in a deterministic context. All our results are robust to the presence of a salvage value. As an application we show that the internal rate of return of any endogenously-interrupted project is essentially unique, even if the project also involves a management problem until its interruption. We also apply our results to the theory of optimal growth and capital deepening and to optimal bankruptcy decisions.
Document Type: 
Working Paper

Files in This Item:
File
Size
254.49 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.