Abstract
In frictionless markets there typically exists a portfolio whose long-term growth rate of wealth almost surely dominates that of any other portfolio. In this note we show that this continues to hold in a Black-Scholes-type market with proportional transaction costs.We heavily rely on results from Gerhold et al. (Financ Stochast 17:325–354 2013 [7]), who determine a portfolio maximizing the expected long-term growth rate of wealth in the same setup.
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Acknowledgements
The authors thank Johannes Muhle-Karbe for fruitful comments and discussions. Moreover, they acknowledge financial support through DFG-Sachbeihilfe KA 1682/4-1.
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Feodoria, MR., Kallsen, J. (2016). Almost Surely Optimal Portfolios Under Proportional Transaction Costs. In: Kallsen, J., Papapantoleon, A. (eds) Advanced Modelling in Mathematical Finance. Springer Proceedings in Mathematics & Statistics, vol 189. Springer, Cham. https://doi.org/10.1007/978-3-319-45875-5_14
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