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This paper studies the multi-period mean-variance portfolio allocationproblem with transaction costs. Many methods have been proposed these lastyears to challenge the famous uni-period Markowitz strategy.But these methodscannot integrate transaction costs or become computationally heavy and hardlyapplicable. In this paper, we try to tackle this allocation problem byproposing an innovative approach which relies on representing the set ofadmissible portfolios by a finite dimensional Wiener chaos expansion. Thisnumerical method is able to find an optimal strategy for the allocation problemsubject to transaction costs. To complete the study, the link between optimalportfolios submitted to transaction costs and the underlying risk aversion isinvestigated. Then a competitive and compliant benchmark based on thesequential uni-period Markowitz strategy is built to highlight the efficiencyof our approach.

Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach