On a class of optimal stopping problems for diffusions with discontinuous coefficients
Ludger Rüschendorf and Mikhail A. Urusov
Source: Ann. Appl. Probab. Volume 18, Number 3
(2008), 847-878.
Abstract
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity assumptions on the coefficients and on the gain function are not satisfied. We apply this method to the optimal stopping of integral functionals with exponential discount of the form Ex ∫0τ e−λsf(Xs) ds, λ≥0 for one-dimensional diffusions X. We prove a general verification theorem which justifies the modified version of the free boundary problem. In the case of no drift and discount, the free boundary problem allows to give a complete and explicit discussion of the stopping problem.
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Keywords: Optimal stopping; free boundary problem; one-dimensional SDE; Engelbert–Schmidt condition; local times; occupation times formula; Itô–Tanaka formula
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1211819787
Digital Object Identifier: doi:10.1214/07-AAP474
Mathematical Reviews number (MathSciNet): MR2418231
Zentralblatt MATH identifier: 1153.60021
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