Alpha mining, which refers to the systematic discovery of data-driven signals predictive of future cross-sectional returns, is a central task in quantitative research. Recent progress in large language models (LLMs) has sparked interest in LLM-based alpha mining frameworks, which offer a promising middle ground between human-guided and fully automated alpha mining approaches and deliver both speed and semantic depth. This study presents a structured review of emerging LLM-based alpha mining systems from an agentic perspective, and analyzes the functional roles of LLMs, ranging from miners and evaluators to interactive assistants. Despite early progress, key challenges remain, including simplified performance evaluation, limited numerical understanding, lack of diversity and originality, weak exploration dynamics, temporal data leakage, and black-box risks and compliance challenges. Accordingly, we outline future directions, including improving reasoning alignment, expanding to new data modalities, rethinking evaluation protocols, and integrating LLMs into more general-purpose quantitative systems. Our analysis suggests that LLM is a scalable interface for amplifying both domain expertise and algorithmic rigor, as it amplifies domain expertise by transforming qualitative hypotheses into testable factors and enhances algorithmic rigor for rapid backtesting and semantic reasoning. The result is a complementary paradigm, where intuition, automation, and language-based reasoning converge to redefine the future of quantitative research.

Optimal execution is a sequential decision-making problem for cost-saving in algorithmic trading. Studies have found that reinforcement learning (RL) can help decide the order-splitting sizes. However, a problem remains unsolved: how to place limit orders at appropriate limit prices? The key challenge lies in the ``continuous-discrete duality'' of the action space. On the one hand, the continuous action space using percentage changes in prices is preferred for generalization. On the other hand, the trader eventually needs to choose limit prices discretely due to the existence of the tick size, which requires specialization for every single stock with different characteristics (e.g., the liquidity and the price range). So we need continuous control for generalization and discrete control for specialization. To this end, we propose a hybrid RL method to combine the advantages of both of them. We first use a continuous control agent to scope an action subset, then deploy a fine-grained agent to choose a specific limit price. Extensive experiments show that our method has higher sample efficiency and better training stability than existing RL algorithms and significantly outperforms previous learning-based methods for order execution.