# Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs

*S\"oren Christensen* and
*Marc Wittlinger*

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**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.

**Date:** 2012-09, Revised 2013-06

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**Persistent link:** https://EconPapers.repec.org/RePEc:arx:papers:1209.0305

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