An optimal stopping problem in a diffusion-type model with delay

Pavel V. Gapeev and Markus Reiss

Statistics & Probability Letters, 2006, vol. 76, issue 6, 601-608

Abstract: We present an explicit solution to an optimal stopping problem in a model described by a stochastic delay differential equation with an exponential delay measure. The method of proof is based on reducing the initial problem to a free-boundary problem and solving the latter by means of the smooth-fit condition. The problem can be interpreted as pricing special perpetual average American put options in a diffusion-type model with delay.

Keywords: Optimal; stopping; Stochastic; delay; differential; equation; Diffusion; process; Sufficient; statistic; Free-boundary; problem; Smooth; fit; Girsanov's; theorem; Ito's; formula (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (5)

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