Discounting and Patience in Optimal Stopping and Control Problems
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 di usions. 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.
|Date of creation:||14 Oct 2009|
|Contact details of provider:|| Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014|
Web page: http://www.kellogg.northwestern.edu/research/math/
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- John K.-H. Quah & Bruno Strulovici, 2009.
"Comparative Statics, Informativeness, and the Interval Dominance Order,"
Econometric Society, vol. 77(6), pages 1949-1992, November.
- John K.-H. Quah & Bruno Strulovici, 2007. "Comparative Statics, Informativeness, and the Interval Dominance Order," Economics Papers 2007-W04, Economics Group, Nuffield College, University of Oxford.
- Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, 01.
- Cripps, Martin William & Keller, R Godfrey & Rady, Sven, 2003. "Strategic Experimentation with Exponential Bandits," CEPR Discussion Papers 3814, C.E.P.R. Discussion Papers.
- Cripps, Martin & Keller, Godfrey & Rady, Sven, 2003. "Strategic Experimentation with Exponential Bandits," Discussion Papers in Economics 4, University of Munich, Department of Economics.
- Gustavo Manso & Bruno Strulovici & Alexei Tchistyi, 2010. "Performance-Sensitive Debt," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 1819-1854.
- Bruno Strulovici, 2010. "Learning While Voting: Determinants of Collective Experimentation," Econometrica, Econometric Society, vol. 78(3), pages 933-971, 05.
- Bruno Strulovici, 2008. "Learning while voting: determinants of collective experimentation," Economics Papers 2008-W08, Economics Group, Nuffield College, University of Oxford.
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