Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs
Abstract
In this paper we investigate a new class of growth rate maximization problems based on impulse control strategies such that the average number of trades per time unit does not exceed a fixed level. Moreover, we include proportional transaction costs to make the portfolio problem more realistic. We provide a Verification Theorem to compute the optimal growth rate as well as an optimal trading strategy. Furthermore, we prove the existence of a constant boundary strategy which is optimal. At the end, we compare our approach to other discrete-time growth rate maximization problems in numerical examples. It turns out that constant boundary strategies with a small average number of trades per unit perform nearly as good as the classical optimal solutions with infinite activity.
Keywords
Cite
@article{arxiv.1209.0305,
title = {Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs},
author = {Sören Christensen and Marc Wittlinger},
journal= {arXiv preprint arXiv:1209.0305},
year = {2013}
}