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The solution of discretionary stopping problems with applications to the optimal timing of investment decisions

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  • Timothy C. Johnson

Abstract

We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting. This is done within a framework based on dynamic programming techniques employing variational inequalities and links to the probabilistic approaches employing $r$-excessive functions and martingale theory. The aim of this paper is to facilitate the the solution of a wide variety of problems, particularly in finance or economics.

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  • Timothy C. Johnson, 2012. "The solution of discretionary stopping problems with applications to the optimal timing of investment decisions," Papers 1210.2617, arXiv.org.
  • Handle: RePEc:arx:papers:1210.2617
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    File URL: http://arxiv.org/pdf/1210.2617
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    1. Lamberton, Damien, 2009. "Optimal stopping with irregular reward functions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3253-3284, October.
    2. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    3. Henderson, Vicky & Hobson, David G., 2002. "Real options with constant relative risk aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 329-355, December.
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