Robust control in financial markets with transaction costs under logarithmic utility functions

The problem of portfolio optimization under logarithmic utilities for Black-Scholes financial markets is considered. The corresponding verification theorem is formulated and optimal consumption/investment strategies are constructed explicitly. Then, based on the Leland-Lepinette approach, these strategies are modified and it is shown that the obtained investment and consumption strategies are optimal in the asymptotic setting when the number of portfolio revisions tends to infinity. Cases of small and large transactions were studied. It is established that the constructed strategies are robust, i.e. stable when market parameters change. The results of Monte Carlo numerical simulation are given which in practice confirm theoretical conclusions. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.

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