Constructing Time-Homogeneous Generalised Diffusions Consistent with Optimal Stopping Values
Probability
2010-05-04 v1 Optimization and Control
Abstract
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the problem value in this setting. In this article we consider an inverse problem; given the set of problem values for a family of objective functions, we aim to recover the diffusion. Under a natural assumption on the family of objective functions we can characterise existence and uniqueness of a diffusion for which the optimal stopping problems have the specified values. The solution of the problem relies on techniques from generalised convexity theory
Cite
@article{arxiv.1005.0160,
title = {Constructing Time-Homogeneous Generalised Diffusions Consistent with Optimal Stopping Values},
author = {David Hobson and Martin Klimmek},
journal= {arXiv preprint arXiv:1005.0160},
year = {2010}
}