Asymptotic methods for transaction costs

Risks, Special Issue: Optimal Investment and Risk Management, Vol. 12 No. 4 (2024), 64 We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is ex...

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Bibliographic Details
Main Author Mayerhofer, Eberhard
Format Journal Article
LanguageEnglish
Published 20.06.2024
Subjects
Mathematics - Probability
Quantitative Finance - Portfolio Management
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Summary:Risks, Special Issue: Optimal Investment and Risk Management, Vol. 12 No. 4 (2024), 64 We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems from optimally tracking benchmarks, hedging the Log contract, to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between trading frequency and trade sizes to have satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity.
DOI:10.48550/arxiv.2407.07100