Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network

ArXiv ID: 2306.08809 “View on arXiv”

Authors: Unknown

Abstract

Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here, we propose a four-step numerical framework for the optimal portfolio execution problem where multiple market regimes exist, with the underlying regime switching based on a Markov process. The market impact costs are modelled with a temporary part and a permanent part, where the former affects only the current trade while the latter persists. Our approach accepts impact cost functions in generic forms. First, we calculate the approximated orthogonal portfolios based on estimated impact cost functions; second, we employ dynamic program to learn the optimal selling schedule of each approximated orthogonal portfolio; third, weights of a neural network are pre-trained with the strategy suggested by previous step; last, we train the neural network to optimize on the original trading model. In our experiment of a 10-asset liquidation example with quadratic impact costs, the proposed combined method provides promising selling strategy for both CRRA (constant relative risk aversion) and mean-variance objectives. The running time is linear in the number of risky assets in the portfolio as well as in the number of trading periods. Possible improvements in running time are discussed for potential large-scale usages.

Keywords: optimal execution, Markov process, market impact, dynamic programming, neural networks, Equities / Portfolio Execution

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats
• Why: The paper proposes a sophisticated four-step framework combining dynamic programming, neural networks, and regime-switching models, involving significant mathematical derivations and numerical methods. However, the experimental section appears to be a limited 10-asset liquidation example with synthetic data, lacking the statistical depth, robust backtesting frameworks, and real-world data validation typically expected for empirically rigorous quant finance.

  flowchart TD
    A["Research Goal<br>Optimal Portfolio Execution<br>in Regime-Switching Market"] --> B["Data & Inputs"]
    
    subgraph B [" "]
        B1["Market Data &<br>Trading Parameters"]
        B2["Regime Parameters<br>Markov Process"]
        B3["Impact Cost Functions<br>Temporary & Permanent"]
    end

    B --> C{"Four-Step Numerical Framework"}

    subgraph C ["Computational Processes"]
        C1["Step 1: Impact Approximation<br>Calculate Orthogonal Portfolios"]
        C2["Step 2: Dynamic Programming<br>Learn Optimal Selling Schedule"]
        C3["Step 3: Neural Network<br>Pre-train with DP Strategy"]
        C4["Step 4: Final Optimization<br>Train NN on Original Model"]
    end

    C --> D["Key Findings & Outcomes"]

    subgraph D [" "]
        D1["Promising Selling Strategy<br>CRRA & Mean-Variance"]
        D2["Linear Running Time<br>O(N) in Assets & Periods"]
        D3["Scalable Framework<br>for Large-Scale Usage"]
    end