Asymptotic methods for transaction costs

ArXiv ID: 2407.07100 “View on arXiv”

Authors: Unknown

Abstract

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.

Keywords: Optimal Trading Strategies, Transaction Costs, Polynomial Approximation, Utility Maximization, Hedging

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is heavily math-centric, featuring advanced asymptotic methods, free boundary problems, and reflected diffusions without any empirical backtests, datasets, or implementation details.

  flowchart TD
    A["Research Goal: Approximate optimal trading strategies with transaction costs"] --> B{"Methodology: Polynomial Approximation"}
    B --> C["Input: Market models & cost structure"]
    B --> D["Input: Objective function e.g. utility or tracking error"]
    C & D --> E["Process: Solve DP/HJB for residual value"]
    E --> F["Process: Approximate solution via polynomial expansion"]
    F --> G["Outcome: Discrete executable trading strategy"]
    G --> H["Key Finding: Optimal trade-off between frequency and size"]