An optimal stopping problem in a diffusion-type model with delay - Pavel V. Gapeev; Markus Reiß (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2005)
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.
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