mlsanityData to 14 Oct 2026

Exploratory Mean-Variance with Jumps: An Equilibrium Approach

arXiv 2512.09224 ↗First posted 10 Dec 2025q-fin.PM stat.MLcited by 0

On the map: Deep reinforcement learning methods → Adversarial robustness and RL in finance

Abstract (arXiv)

Revisiting the continuous-time Mean-Variance (MV) Portfolio Optimization problem, we model the market dynamics with a jump-diffusion process and apply Reinforcement Learning (RL) techniques to facilitate informed exploration within the control space. We recognize the time-inconsistency of the MV problem and adopt the time-inconsistent control (TIC) approach to analytically solve for an exploratory equilibrium investment policy, which is a Gaussian distribution centered on the equilibrium control of the classical MV problem. Our approach accounts for time-inconsistent preferences and actions, and our equilibrium policy is the best option an investor can take at any given time during the investment period. Moreover, we leverage the martingale properties of the equilibrium policy, design a RL model, and propose an Actor-Critic RL algorithm. All of our RL model parameters converge to the corresponding true values in a simulation study. Our numerical study on 24 years of real market data shows that the proposed RL model is profitable in 13 out of 14 tests, demonstrating its practical applicability in real world investment.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods. Builds on 6 of its 43 references that are in the map. First posted on arXiv 10 Dec 2025.

Builds on

6 of 43 references.

Closest ancestors · 2

Same direction, newest first

  1. 2025Exploratory Mean-Variance Portfolio Optimization with Regime-Switching Market Dynamics28 Jan
  2. 2024Reinforcement Learning for Jump-Diffusions, with Financial Applications26 May

Other references · 4

  1. 2021Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithmscited by 101
  2. 2022q-Learning in Continuous Timecited by 91
  3. 2021Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approachcited by 84
  4. 2017Using simulation studies to evaluate statistical methodscited by 49

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2024Mean--Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study
  2. 2026Dynamic mean-variance portfolio selection with no-shorting constraints and unknown investment opportunity sets
  3. 2025Multi-period Asset-liability Management with Reinforcement Learning in a Regime-Switching Market
  4. 2025A non-zero-sum game with reinforcement learning under mean-variance framework
  5. 2026Deterministic Policy Gradient for Learning Equilibrium in Time-Inconsistent Control Problems
  6. 2026Reinforcement Learning for Dividend Optimization in Partially Observed Regime-Switching Diffusion Model
  7. 2024Deep Reinforcement Learning and Mean-Variance Strategies for Responsible Portfolio Optimization
  8. 2026Exploratory Randomization for Discrete-Time Risk-Sensitive Benchmarked Investment Management with Reinforcement Learning