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Multi-Agent Regime-Conditioned Diffusion (MARCD) for CVaR-Constrained Portfolio Decisions

Ali Atiah Alzahrani

TL;DR

MARCD addresses non-stationarity and regime shifts in portfolio decisions by coupling a $K$-state Gaussian HMM with a regime-conditioned diffusion generator and a CVaR-epigraph allocator under strict walk-forward governance. It introduces a tail-weighted diffusion objective and a regime-aware MoE denoiser to strengthen left-tail co-movements and crisis fidelity, linking scenario generation directly to decisions. In out-of-sample tests on daily data from 2005–2025, MARCD reduces MaxDD by about 34% relative to Black-Litterman while maintaining or improving Sharpe, and it offers an auditable, constraint-governed pipeline suitable for risk management. The results suggest decision-aware generative modeling can meaningfully improve tail control and decision quality in financial portfolios, with practical governance benefits and room for end-to-end differentiation and faster inference in future work.

Abstract

We examine whether regime-conditioned generative scenarios combined with a convex CVaR allocator improve portfolio decisions under regime shifts. We present MARCD, a generative-to-decision framework with: (i) a Gaussian HMM to infer latent regimes; (ii) a diffusion generator that produces regime-conditioned scenarios; (iii) signal extraction via blended, shrunk moments; and (iv) a governed CVaR epigraph quadratic program. Contributions: Within the Scenario stage we introduce a tail-weighted diffusion objective that up-weights low-quantile outcomes relevant for drawdowns and a regime-expert (MoE) denoiser whose gate increases with crisis posteriors; both are evaluated end-to-end through the allocator. Under strict walk-forward on liquid multi-asset ETFs (2005-2025), MARCD exhibits stronger scenario calibration and materially smaller drawdowns: MaxDD 9.3% versus 14.1% for BL (a 34% reduction) over 2020-2025 out-of-sample. The framework provides an auditable pipeline with explicit budget, box, and turnover constraints, demonstrating the value of decision-aware generative modeling in finance.

Multi-Agent Regime-Conditioned Diffusion (MARCD) for CVaR-Constrained Portfolio Decisions

TL;DR

MARCD addresses non-stationarity and regime shifts in portfolio decisions by coupling a -state Gaussian HMM with a regime-conditioned diffusion generator and a CVaR-epigraph allocator under strict walk-forward governance. It introduces a tail-weighted diffusion objective and a regime-aware MoE denoiser to strengthen left-tail co-movements and crisis fidelity, linking scenario generation directly to decisions. In out-of-sample tests on daily data from 2005–2025, MARCD reduces MaxDD by about 34% relative to Black-Litterman while maintaining or improving Sharpe, and it offers an auditable, constraint-governed pipeline suitable for risk management. The results suggest decision-aware generative modeling can meaningfully improve tail control and decision quality in financial portfolios, with practical governance benefits and room for end-to-end differentiation and faster inference in future work.

Abstract

We examine whether regime-conditioned generative scenarios combined with a convex CVaR allocator improve portfolio decisions under regime shifts. We present MARCD, a generative-to-decision framework with: (i) a Gaussian HMM to infer latent regimes; (ii) a diffusion generator that produces regime-conditioned scenarios; (iii) signal extraction via blended, shrunk moments; and (iv) a governed CVaR epigraph quadratic program. Contributions: Within the Scenario stage we introduce a tail-weighted diffusion objective that up-weights low-quantile outcomes relevant for drawdowns and a regime-expert (MoE) denoiser whose gate increases with crisis posteriors; both are evaluated end-to-end through the allocator. Under strict walk-forward on liquid multi-asset ETFs (2005-2025), MARCD exhibits stronger scenario calibration and materially smaller drawdowns: MaxDD 9.3% versus 14.1% for BL (a 34% reduction) over 2020-2025 out-of-sample. The framework provides an auditable pipeline with explicit budget, box, and turnover constraints, demonstrating the value of decision-aware generative modeling in finance.

Paper Structure

This paper contains 30 sections, 22 theorems, 29 equations, 4 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Method Overview and Rationale
  5. Method Overview and Rationale
  6. Regime Detection (strict walk-forward)
  7. Regime-Conditioned Diffusion
  8. Allocation Agent: CVaR Epigraph Program and Properties
  9. Note.
  10. Tail-Weighted Diffusion Loss
  11. Regime-MoE Denoiser
  12. Theory Highlights
  13. Experimental setup
  14. Results and discussion
  15. Ablations and Component Analyses
  16. ...and 15 more sections

Key Result

Theorem 1

Minimizing $L_{\text{tail}}$ in Eq. (7) controls a spectral-risk upper bound on the decision-relevant CVaR generalization gap for any feasible portfolio $w$, scaling with $(1-\alpha)^{-1}$ and the denoising error on the lower-$q$ tail.

Figures (4)

  • Figure 1: Multi-Agent Regime-Conditioned Diffusion (MARCD).
  • Figure 2: OOS cumulative NAV, drawdown, and HMM regime posteriors ($K{=}3$).
  • Figure 3: Ablations—performance and diagnostic metrics across variants (OOS 2020--2025).
  • Figure 4: Profiles---performance and diagnostics summary (OOS 2020--2025).

Theorems & Definitions (39)

  • Theorem 1: Spectral CVaR Control by Tail-Weighted Diffusion; App. A.11
  • Theorem 2: MoE Oracle, Consistency & Stability; App. A.13
  • Theorem 3: Allocator Lipschitzness & Regret; App. A.14
  • Proposition 1: Spectral risk proxy for portfolio tail functionals
  • proof : Sketch
  • Remark 1: Decision relevance
  • Proposition 2: Closed-form effective sample size (ESS)
  • proof
  • Remark 2: Choosing $(q,\eta)$
  • Theorem 4: MoE oracle risk decomposition
  • ...and 29 more