In this paper we investigate a new class of growth rate maximization problemsbased on impulse control strategies such that the average number of trades pertime unit does not exceed a fixed level. Moreover, we include proportionaltransaction costs to make the portfolio problem more realistic. We provide aVerification Theorem to compute the optimal growth rate as well as an optimaltrading strategy. Furthermore, we prove the existence of a constant boundarystrategy which is optimal. At the end, we compare our approach to otherdiscrete-time growth rate maximization problems in numerical examples. It turnsout that constant boundary strategies with a small average number of trades perunit perform nearly as good as the classical optimal solutions with infiniteactivity.
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