Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach

ArXiv ID: 2305.16152 “View on arXiv”

Authors: Unknown

Abstract

This paper studies the multi-period mean-variance portfolio allocation problem with transaction costs. Many methods have been proposed these last years to challenge the famous uni-period Markowitz strategy.But these methods cannot integrate transaction costs or become computationally heavy and hardly applicable. In this paper, we try to tackle this allocation problem by proposing an innovative approach which relies on representing the set of admissible portfolios by a finite dimensional Wiener chaos expansion. This numerical method is able to find an optimal strategy for the allocation problem subject to transaction costs. To complete the study, the link between optimal portfolios submitted to transaction costs and the underlying risk aversion is investigated. Then a competitive and compliant benchmark based on the sequential uni-period Markowitz strategy is built to highlight the efficiency of our approach.

Keywords: Portfolio Allocation, Mean-Variance Optimization, Transaction Costs, Wiener Chaos Expansion, Asset Management

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic analysis and Wiener chaos expansions, involving heavy mathematical derivations and theoretical frameworks, while presenting no empirical data, code, or backtesting results, focusing solely on theoretical propositions and computational method design.

  flowchart TD
    A["Research Goal:<br>Multi-period Mean-Variance<br>Portfolio Optimization with<br>Transaction Costs"] --> B{"Key Methodology"};
    B --> C["Wiener Chaos Expansion<br>for Admissible Portfolios"];
    B --> D["Sequential Single-Period<br>Markowitz Benchmark"];
    
    C --> E["Computational Process:<br>Finite Dimensional Approximation<br>Optimal Strategy Derivation"];
    D --> E;
    
    E --> F["Data/Inputs:<br>Asset Return Scenarios<br>Risk Aversion Parameters<br>Transaction Cost Structures"];
    
    F --> G{"Key Findings/Outcomes"};
    G --> H["Efficient Optimal Strategy<br>Integrated Transaction Costs"];
    G --> I["Risk Aversion Impact<br>Analysis on Portfolio Allocation"];
    G --> J["Competitive Benchmark<br>Validating Approach Efficiency"];