Approximating Optimal Trading with Proportional Transaction Costs

Summary

The document presents an approximation method for finding optimal strategies when trades incur proportional transaction costs. It represents the residual value function with a polynomial approximation, providing a way to handle problems where the exact solution may be difficult to obtain.

The method is illustrated in benchmark tracking, hedging a Log contract, and maximizing utility from terminal wealth. It also translates theoretical strategies, which may involve continuous trading with infinite activity, into discrete trades that can be executed in practice. The central implementation issue is balancing how often to trade against the size of each trade so that the discrete strategy remains close to the theoretical optimum. The excerpt describes the approach and application areas but supplies no numerical comparisons, assumptions, or performance results, so its accuracy and practical effectiveness cannot be judged from the summary alone.

Key ideas

• A polynomial approximation of the residual value function can be used to approximate strategies under proportional transaction costs.
• The approach is demonstrated for benchmark tracking, Log contract hedging, and terminal-wealth utility maximization.
• The theoretical strategies may entail continuous trading with infinite activity.
• Practical discrete trades require a balance between trading frequency and trade size.
• The excerpt provides no quantitative evidence on approximation accuracy or realized performance.

Tags

# Asymptotic methods for transaction costs


# Asymptotic methods for transaction costs









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.