Paper: arXiv 2604.27700

Authors: Chiheb Ben Hammouda, Michael Samet, Raúl Tempone

Abstract

The rapid growth of weather-dependent renewable generation increases price volatility and imbalance penalty risk in power markets, creating the need for advanced quantitative trading strategies. We develop a data-driven continuous-time stochastic optimal control framework for intraday electricity trading using stochastic differential equations with drift terms ensuring mean reversion to deterministic forecast trajectories. Production follows a Jacobi diffusion, while prices follow an asymmetric jump-diffusion to reflect the heavy-tailed behavior observed in intraday markets. The framework accounts for realistic market features by incorporating gate closure and energy-based imbalance settlement over the delivery window, where the path-dependent imbalance cost is handled by state augmentation to preserve the Markovian structure. The value function is characterized via the dynamic programming principle by a three-stage sequence of two linear Kolmogorov backward equations and a nonlinear Hamilton-Jacobi-Bellman partial integro-differential equation. To solve this problem efficiently, we propose a monotone IMEX finite-difference scheme with operator splitting, semi-implicit linearization, and a differential formulation for the jump operator. Numerical experiments based on German market data indicate that, under the provided forecasts, the computed strategy outperforms the TWAP benchmark and approaches the perfect-foresight benchmark. Sensitivity experiments further show how jump intensity, delivery-window length, and trading horizon affect the trading policy and the resulting profit-and-loss distribution.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous continuous-time stochastic control model using Jacobi diffusions, asymmetric jump-diffusions, and a three-stage HJB PIDE system. The empirical validation using German intraday electricity market data demonstrates practical trading improvements against TWAP benchmarks.

Research Flowchart

  flowchart TD
    A[Goal: Optimize Intraday Electricity Trading & Manage Imbalance Risk] --> B[Input Data: German Market Data & Renewable Forecasts]
    B --> C[Model Formulation: SDEs for Production & Price with State Augmentation]
    C --> D[Control Framework: 3-Stage Sequence of Backward PDEs & HJB PIDE]
    D --> E[Numerical Solution: Monotone IMEX Scheme with Operator Splitting]
    E --> F[Outcomes: Outperforms TWAP & Approaches Perfect-Foresight Benchmark]

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0 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.