Paper: arXiv 2609.35086

Authors: Kelvin J. L. Koa, Xinyang Li, Ke-Wei Huang

Abstract

In this work, we study portfolio optimization under the stochastic discount factor (SDF) framework by learning market state representations that capture the underlying risk structures of financial data. This is challenging due to several factors: financial markets exhibit non-stationary dynamics with shifting regimes, multimodal inputs such as price and news data often contain stochastic noise, and existing diffusion-based approaches, while effective for modeling stochastic dynamics, rely on assumptions such as isotropic Gaussian noise that fail to capture the state-dependent nature of financial uncertainty. To address these challenges, we introduce RADAR, a retrieval-augmented diffusion framework that learns market representations by conditioning on similar historical regimes. RADAR leverages retrieval to construct context-dependent noise distributions, applies conditional diffusion to denoise multimodal representations, and initializes the diffusion process using empirical statistics to reflect state-dependent uncertainty. Experiments show that RADAR achieves state-of-the-art performance on key risk-adjusted metrics while producing economically meaningful signals on asset returns and correlations.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly novel approach by integrating retrieval-augmented diffusion models for SDF-based portfolio optimization, addressing key challenges in financial modeling. It demonstrates strong empirical results with state-of-the-art performance and provides code for reproducibility, making it a significant contribution.

Research Flowchart

  flowchart TD
    A[Research Goal: Portfolio Optimization under SDF] --> B{Challenges: Non-stationary, Multimodal Noise, Isotropic Diffusion Limits};

    B --> C[Methodology: RADAR Framework];

    C --> D{Data/Inputs: Price Data, News Data};

    D --> E[Computational Processes: Retrieval-Augmented Diffusion, Conditional Diffusion, Empirical Statistics Init.];

    E --> F[Key Findings/Outcomes: SOTA Risk-Adjusted Metrics, Economically Meaningful Signals];