A capped optimal stopping problem for the maximum process
Probability
2012-04-17 v1 Optimization and Control
Abstract
This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Levy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem, which has its origins in mathematical finance, and provide semi-explicit solutions in terms of scale functions. The optimal stopping boundary is characterised by an ordinary first-order differential equation involving scale functions and, in particular, changes according to the path variation of X. Furthermore, we will link these capped problems to Peskir's maximality principle.
Cite
@article{arxiv.1204.3119,
title = {A capped optimal stopping problem for the maximum process},
author = {Andreas E. Kyprianou and Curdin Ott},
journal= {arXiv preprint arXiv:1204.3119},
year = {2012}
}