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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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    References listed on IDEAS

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    1. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 315-337, December.
    2. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    3. Lamberton, Damien, 2009. "Optimal stopping with irregular reward functions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3253-3284, October.
    4. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    5. 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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