An approximate characterisation of optimal stopping boundaries

Abstract

An identity, of the type of Green's equation, is deduced for the loss function of a stopping process. This yields a set of relations determining the optimal (minimal loss) stopping boundary, which do not require simultaneous determination of the loss function in the stopping region. A no-overshoot approximation is invoked, but a bound on the magnitude of the terms neglected is obtained by appeal to a general version of Chernoff's tangency condition at an optimal boundary.