CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

From Risk-Neutral to Risk-Sensitive Reinforcement Learning: Actor–Critic vs REINFORCE with Tail-Based Risk Measures

Aprida Siska Lestia (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Yogyakarta Department of Mathematics, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat University, South Kalimantan)
Adhitya Ronnie Effendie (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Yogyakarta)
Made Tantrawan (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Yogyakarta)
Muhammad Rafli Azrarsyah (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Yogyakarta)



Article Info

Publish Date
30 May 2026

Abstract

This study investigates risk-sensitive reinforcement learning (RL) for portfolio decision-making under empirically heavy-tailed return distributions. We compare two policy-gradient architectures—REINFORCE with baseline (REINFORCE-BL) and batched Advantage Actor–Critic (A2C-B)—and examine how tail-based risk measures modify learning dynamics and robustness. Quantitative diagnostics confirm substantial excess kurtosis and strong rejection of normality in daily NASDAQ returns, motivating the integration of tail-sensitive objectives. Risk sensitivity is introduced at the episodic level through penalties based on Value at Risk (VaR), Conditional Value at Risk (CVaR), and Entropic Value at Risk (EVaR) at the 95% confidence level. Experiments are conducted in a multi-asset portfolio exposure-control environment, with performance evaluated across multiple random seeds using both training dynamics and out-of-sample financial metrics (CAGR, volatility, Sharpe ratio, drawdown, and realized tail risk). Results show that while both architectures perform comparably under the risk-neutral objective, actor–critic learning exhibits greater stability and lower dispersion under coherent tail penalties. In particular, CVaR and EVaR objectives lead to smoother convergence and reduced instability compared to VaR, especially for A2C-B. Statistical tests indicate that performance differences become more pronounced under coherent tail-risk objectives. These findings highlight the interaction between heavy-tailed environments, coherent risk measures, and algorithmic architecture, suggesting that actor–critic methods provide a more robust foundation for risk-sensitive RL in financial settings exposed to extreme events.

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Journal Info

Abbrev

Math

Publisher

Subject

Mathematics

Description

Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh ...