Agostino Capponi

Agostino Capponi, Mihailo Stojnic

In this paper, we revisit and further explore a mathematically rigorous connection between Causal inference (C-inf) and the Low-rank recovery (LRR) established in [10]. Leveraging the Random duality - Free probability theory (RDT-FPT) connection, we obtain the exact explicit typical C-inf asymmetric phase transitions (PT). We uncover a doubling low-rankness phenomenon, which means that exactly two times larger low rankness is allowed in asymmetric scenarios compared to the symmetric worst case ones considered in [10]. Consequently, the final PT mathematical expressions are as elegant as those obtained in [10], and highlight direct relations between the targeted C-inf matrix low rankness and the time of treatment. Our results have strong implications for applications, where C-inf matrices are not necessarily symmetric.

Agostino Capponi, Mihailo Stojnic

In this paper we establish a mathematically rigorous connection between Causal inference (C-inf) and the low-rank recovery (LRR). Using Random Duality Theory (RDT) concepts developed in [46,48,50] and novel mathematical strategies related to free probability theory, we obtain the exact explicit typical (and achievable) worst case phase transitions (PT). These PT precisely separate scenarios where causal inference via LRR is possible from those where it is not. We supplement our mathematical analysis with numerical experiments that confirm the theoretical predictions of PT phenomena, and further show that the two closely match for fairly small sample sizes. We obtain simple closed form representations for the resulting PTs, which highlight direct relations between the low rankness of the target C-inf matrix and the time of the treatment. Hence, our results can be used to determine the range of C-inf's typical applicability.

Agostino Capponi, Alfio Gliozzo, Brian Zhu

Prediction markets allow users to trade on outcomes of real-world events, but are prone to fragmentation through overlapping questions, implicit equivalences, and hidden contradictions across markets. We present an agentic AI pipeline that autonomously (i) clusters markets into coherent topical groups using natural-language understanding over contract text and metadata, and (ii) identifies within-cluster market pairs whose resolved outcomes exhibit strong dependence, including same-outcome (correlated) and different-outcome (anti-correlated) relationships. Using a historical dataset of resolved markets on Polymarket, we evaluate the accuracy of the agent's relational predictions. We then translate discovered relationships into a simple trading strategy to quantify how these relationships map to actionable signals. Results show that agent-identified relationships achieve roughly 60-70% accuracy, and their induced trading strategies earn about 20% average returns over week-long horizons, highlighting the ability of agentic AI and large language models to uncover latent semantic structure in prediction markets.

Graeme Baker, Agostino Capponi, J. Antonio Sidaoui

We propose a data-driven dynamic factor framework where a response variable depends on a high-dimensional set of covariates, without imposing any parametric model on the joint dynamics. Leveraging Anisotropic Diffusion Maps, a nonlinear manifold learning technique introduced by Singer and Coifman, our framework uncovers the joint dynamics of the covariates and responses in a purely data-driven way. We approximate the embedding dynamics using linear diffusions, and exploit Kalman filtering to predict the evolution of the covariates and response variables directly from the diffusion map embedding space. We generalize Singer's convergence rate analysis of the graph Laplacian from the case of independent uniform samples on a compact manifold to the case of time series arising from Langevin diffusions in Euclidean space. Furthermore, we provide rigorous justification for our procedure by showing the robustness of approximations of the diffusion map coordinates by linear diffusions, and the convergence of ergodic averages under standard spectral assumptions on the underlying dynamics. We apply our method to the stress testing of equity portfolios using a combination of financial and macroeconomic factors from the Federal Reserve's supervisory scenarios. We demonstrate that our data-driven stress testing method outperforms standard scenario analysis and Principal Component Analysis benchmarks through historical backtests spanning three major financial crises, achieving reductions in mean absolute error of up to 55% and 39% for scenario-based portfolio return prediction, respectively.

Fengpei Li, Haoxian Chen, Jiahe Lin et al.

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations often become computationally prohibitive, especially for nested, multi-level, or path-dependent evaluations lacking effective variance reduction techniques. While machine learning (ML) surrogates appear as natural alternatives, naive replacements typically introduce unquantifiable biases. We address this challenge by introducing Prediction-Enhanced Monte Carlo (PEMC), a framework that leverages modern ML models as learned predictors, using cheap and parallelizable simulation as features, to output unbiased evaluation with reduced variance and runtime. PEMC can also be viewed as a "modernized" view of control variates, where we consider the overall computation-cost-aware variance reduction instead of per-replication reduction, while bypassing the closed-form mean function requirement and maintaining the advantageous unbiasedness and uncertainty quantifiability of Monte Carlo. We illustrate PEMC's broader efficacy and versatility through three examples: first, equity derivatives such as variance swaps under stochastic local volatility models; second, interest rate derivatives such as swaption pricing under the Heath-Jarrow-Morton (HJM) interest-rate model. Finally, we showcase PEMC in a socially significant context - ambulance dispatch and hospital load balancing - where accurate mortality rate estimates are key for ethically sensitive decision-making. Across these diverse scenarios, PEMC consistently reduces variance while preserving unbiasedness, highlighting its potential as a powerful enhancement to standard Monte Carlo baselines.

Agostino Capponi, Alfio Gliozzo, Chunghyun Han et al.

This paper presents a first empirical study of agentic AI as autonomous decision-makers in decentralized governance. Using more than 3K proposals from major protocols, we build an agentic AI voter that interprets proposal contexts, retrieves historical deliberation data, and independently determines its voting position. The agent operates within a realistic financial simulation environment grounded in verifiable blockchain data, implemented through a modular composable program (MCP) workflow that defines data flow and tool usage via Agentics framework. We evaluate how closely the agent's decisions align with the human and token-weighted outcomes, uncovering strong alignments measured by carefully designed evaluation metrics. Our findings demonstrate that agentic AI can augment collective decision-making by producing interpretable, auditable, and empirically grounded signals in realistic DAO governance settings. The study contributes to the design of explainable and economically rigorous AI agents for decentralized financial systems.

Humoud Alsabah, Agostino Capponi, Octavio Ruiz Lacedelli et al.

We introduce a reinforcement learning framework for retail robo-advising. The robo-advisor does not know the investor's risk preference, but learns it over time by observing her portfolio choices in different market environments. We develop an exploration-exploitation algorithm which trades off costly solicitations of portfolio choices by the investor with autonomous trading decisions based on stale estimates of investor's risk aversion. We show that the algorithm's value function converges to the optimal value function of an omniscient robo-advisor over a number of periods that is polynomial in the state and action space. By correcting for the investor's mistakes, the robo-advisor may outperform a stand-alone investor, regardless of the investor's opportunity cost for making portfolio decisions.

Agostino Capponi, Reza Ghanadan, Matt Stern

Autonomous systems can substantially enhance a human's efficiency and effectiveness in complex environments. Machines, however, are often unable to observe the preferences of the humans that they serve. Despite the fact that the human's and machine's objectives are aligned, asymmetric information, along with heterogeneous sensitivities to risk by the human and machine, make their joint optimization process a game with strategic interactions. We propose a framework based on risk-sensitive dynamic games; the human seeks to optimize her risk-sensitive criterion according to her true preferences, while the machine seeks to adaptively learn the human's preferences and at the same time provide a good service to the human. We develop a class of performance measures for the proposed framework based on the concept of regret. We then evaluate their dependence on the risk-sensitivity and the degree of uncertainty. We present applications of our framework to self-driving taxis, and robo-financial advising.