Shadow prices for continuous processes
Portfolio Management
2015-05-06 v2 Optimization and Control
Abstract
In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredients are the continuity of the price process and the hypothesis of "no unbounded profit with bounded risk". A counter-example reveals that these hypotheses cannot be relaxed.
Keywords
Cite
@article{arxiv.1408.6065,
title = {Shadow prices for continuous processes},
author = {Christoph Czichowsky and Walter Schachermayer and Junjian Yang},
journal= {arXiv preprint arXiv:1408.6065},
year = {2015}
}