Corpus ID: 235731884

A Note on Utility Maximization with Proportional Transaction Costs and Stability of Optimal Portfolios

@inproceedings{Bayraktar2021ANO,
  title={A Note on Utility Maximization with Proportional Transaction Costs and Stability of Optimal Portfolios},
  author={Erhan Bayraktar and Christoph Czichowsky and Leonid Dolinskyi and Yan Dolinsky},
  year={2021}
}
The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The main idea of our proof is to establish a uniqueness result for the optimal strategy. The proof of the uniqueness is heavily based on the dual approach which was developed recently in [6, 7, 8]. Mathematical Subject Classification (2010): 91B16, 91G10 

References

SHOWING 1-10 OF 20 REFERENCES
The asymptotic elasticity of utility functions and optimal investment in incomplete markets
The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary andExpand
Duality theory for portfolio optimisation under transaction costs
We consider the problem of portfolio optimisation with general cadlag price processes in the presence of proportional transaction costs. In this context, we develop a general duality theory. InExpand
Shadow Prices for Continuous Processes
In a nancial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sucient conditions for theExpand
The fundamental theorem of asset pricing under transaction costs
This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes.The robust no freeExpand
Consumption-investment problem with transaction costs for Lévy-driven price processes
TLDR
It is proved that the Bellman function of the problem is a viscosity solution of an HJB equation, and a uniqueness theorem for the solution of the latter is established. Expand
Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs
TLDR
Imposing (arbitrarily small) proportional transaction costs and considering logarithmic utility optimisers, it is able to show the existence of a semimartingale, frictionless shadow price process for an exponential fractional Brownian financial market. Expand
Asymptotic Theory of Transaction Costs
The present lecture notes are based on several advanced courses which I gave at the University of Vienna between 2011 and 2013. In 2015 I gave a similar course (“Nachdiplom-Vorlesung”) at ETH Zürich.Expand
Asymptotic arbitrage with small transaction costs
We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λn onExpand
No Arbitrage Under Transaction Costs, with Fractional Brownian Motion and Beyond
We establish a simple no-arbitrage criterion that reduces the absence of arbitrage opportunities under proportional transaction costs to the condition that the asset price process may moveExpand
Sticky Continuous Processes have Consistent Price Systems
TLDR
It is shown that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proportional transaction costs, if it satisfies a natural multi-dimensional generalization of the stickiness condition introduced by Guasoni. Expand
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