CDAM: Computational, Discrete and Applicable Mathematics@LSE

 CDAM Research Report, LSE-CDAM-2009-03

May 2009

Discounted optimal stopping for diffusions: free-boundary versus martingale approach

Pavel V. Gapeev and Hans Rudolf Lerche

The free-boundary and the martingale approach are competitive methods of solving discounted optimal stopping problems for one-dimensional time-homogeneous regular dif- fusion processes on in nite time intervals. We provide a missing link showing the equiva- lence of these approaches for a problem, where the optimal stopping time is equal to the rst exit time of the underlying process from a region restricted by two constant bound- aries. We also consider several illustrating examples including the rational valuation of the perpetual American strangle option.

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