Climate-Dyna Deep Hedging for XVAs: Model-Based Reinforcement Learning, Residual Climate HVA, and Hedge-Instrument Discovery

Risk-aware Q-learning (RaQL) provides a model-free, two-timescale estimator for dynamic risk objectives, but its finite-budget behavior remains fragile: fixed inner-loop hyperparameters can produce unstable value estimates, persistent Bellman residuals, and inefficient sample reuse. This paper proposes an adaptive training controller for Conditional Value-at-Risk (CVaR) RaQL and evaluates it on a daily Bitcoin trading task. The controller preserves the original CVaR estimator and Bellman fixed point; instead, it redesigns the training procedure through six coordinated mechanisms: per-cell inner-step sizing, outer-rate-matched decay synchronization, a short early correction for the VaR-like inner variable, a coverage-first-then-greedy sample allocation rule, progressive suffix aggregation of mature inner estimates, and data-driven calibration of key scales from online-observable quantities. Across 20 random seeds and 856,000 inner-transition samples, the controller reduces the mean empirical CVaR Bellman residual by approximately 85% relative to the fixed-parameter baseline (MeanBEQ: 1.2202 to 0.1854; MeanBEV: 1.1624 to 0.0535) and maintains stability across CVaR levels, discount factors, and training budgets. On the chronological out-of-sample test set, the learned policy attains a Sharpe ratio of 0.9281 with a maximum drawdown of 6.46% after transaction costs. Although buy-and-hold yields a higher cumulative return (35.43% vs. 23.61%), the adaptive policy achieves far lower volatility (9.57% vs. 47.93%), drawdown, and CVaR loss. These results demonstrate that adaptive finite-budget training design, applied solely to the training procedure without altering the risk objective, can materially improve the reliability and risk-adjusted performance of risk-aware Q-learning in financial applications.

Learning accurate value functions plays a decisive role for reinforcement learning (RL) agents to solve long-horizon, complex tasks. Conventional temporal-difference (TD) learning objectives suffer from value-estimation bias that accumulates over the horizon, while extended-horizon modeling methods, such as n-step TD backups and Q-chunking, adopt a rigid, fixed-horizon value-modeling recipe that is often not flexible enough to capture complex value structures in long-horizon, multi-stage tasks. In this paper, we show that enabling value updates with dynamic horizon composition can yield a strong offline policy learning scheme. Our method, Horizon Adaptive Offline Policy Learning via VAlue STitching (VAST), replaces fixed-horizon backups with recursive, horizon-adaptive value composition. Its key ingredient is to couple value optimization with a future state- and horizon-length-conditioned auxiliary value function that is learned through direct data supervision, and a stitching policy that optimally selects the reward-maximizing horizon length and future sub-goal to achieve horizon-adaptive value stitching. This design enables direct estimation and compositional "stitching" of variable-length returns grounded in actionable sub-goal states, providing an accurate and greedily exploitable value-supervision signal for offline policy optimization. Across 50 tasks on OGBench, VAST outperforms fixed-step, extended-horizon methods, and generative-value offline RL baselines, achieving strong performance particularly in high-complexity, long-horizon decision-making tasks.

We propose the first deep learning algorithm, the Certainty Equivalent Learning (CEL) algorithm, for solving high-dimensional discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is numerically challenging because the recursive utility does not have an explicit representation and the Bellman equation contains a certainty equivalent that is difficult to evaluate. The CEL algorithm learns this certainty-equivalent value directly with neural networks and jointly approximates value functions, policy functions, and certainty-equivalent functions. The CEL algorithm is mesh-free and simulation-based, allowing high-dimensional state and control spaces, and does not rely on Euler equations, first-order conditions, or differentiability of the state transition function. The CEL algorithm also works for dynamic programming problems with expected utility as expected utility is a special case of recursive utility. We apply the CEL to discounted linear exponential quadratic Gaussian control, small-noise robust control, Epstein-Zin DSGE, and multivariate strategic asset allocation problems. Compared with closed-form and VFI-based benchmarks, the CEL delivers accurate value and policy approximations, remains effective in high-dimensional problems, achieves accuracy comparable to VFI in the small-noise robust-control case, and produces out-of-sample Bellman errors and Euler or first-order residuals that are in the range from 1.0e-4 to 1.0e-3 for most problems.