On the Optimal Stopping of a One-dimensional Diffusion
Abstract
We consider a one-dimensional diffusion which solves a stochastic differential equation with Borel-measurable coefficients in an open interval. We allow for the endpoints to be inaccessible or absorbing. Given a Borel-measurable function that is uniformly bounded away from 0, we establish a new analytic representation of the -potential of a continuous additive functional of the diffusion. We also characterize the value function of an optimal stopping problem with general reward function as the unique solution of a variational inequality (in the sense of distributions) with appropriate growth or boundary conditions. Furthermore, we establish several other characterisations of the solution to the optimal stopping problem, including a generalisation of the so-called "principle of smooth fit".
Cite
@article{arxiv.1207.5491,
title = {On the Optimal Stopping of a One-dimensional Diffusion},
author = {Damien Lamberton and Mihail Zervos},
journal= {arXiv preprint arXiv:1207.5491},
year = {2014}
}