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

2012/10/09 by Timothy C. Johnson, Johnson, Timothy C.
Economics, Econometrics and Finance · Mathematics · #49K45 #60G40 (Primary) 93E20 #90C39 (Secondary) #91B70 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #math.PR #msc:49K45 #msc:60G40 #msc:90C39 #msc:91B70 #msc:93E20 #q-fin.CP

paper · pdf · doi:10.48550/arxiv.1210.2617

arxiv created 2012/10/09 · arxiv updated 2012/10/10

Abstract

We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, Itô 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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