Proposals for 2027 entry
These are the PhD projects available for the April and October 2027 intakes. Each has a reference. Select up to three, in order of preference, and quote their references in your project title as set out under Admissions. If you propose your own topic instead, your title ends with (QRT Labs) alone. For more detail on a project, contact its supervisor.
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2027-JB-1
Generative Pretraining with Population Rewards via Wasserstein Transport
Supervisor: Joey Bose
Description
Generative models are typically pretrained to reproduce an observed data distribution, with reward signals incorporated through subsequent post-training or inference-time steering. However, weak supervision often describes desirable properties of an entire population without providing examples from the distribution we wish to generate. We formulate population-supervised generative learning, in which reference examples and distributional rewards jointly specify the training target through a Wasserstein-regularized variational problem. The resulting target is characterized by a self-consistent transport kernel: reference examples undergo spatial corrections coordinated by shared population feedback. For concave functions of feature expectations, we derive global optimality conditions; for quadratic population discrepancies, we obtain a strongly convex finite-dimensional dual and an explicit optimality certificate. These characterizations motivate a direct mean-field particle algorithm that optimizes the empirical coupling objective without maintaining dual variables, with a descent guarantee under suitable regularity and step-size conditions. An exactly solvable mean-correction problem illustrates how population supervision can revise aggregate statistics while preserving the centered distribution. Finally, we use the evolving particle population as training endpoints for flow matching, incorporating reward information during generative pretraining. The trained model generates independently of the reward oracle, while the Wasserstein cost explicitly determines which departures from the reference population are preferred.
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2027-CT-1
Scalable, Stable, and Privacy-Preserving Learning Algorithms
Supervisor: Calvin Tsay
Description
Training large models on sensitive or proprietary data requires mitigating noise, adversarial perturbations, and privacy leakage. However, building these guarantees into training usually breaks down at scale. This project studies optimisation algorithms that integrate differential-privacy and stability guarantees directly into the training loop, using structure-exploiting bounding methods that can scale large models. Specifically, building on the group's work on certified training, you'll deploy these certificates in a "search" for scalable, stable, and privacy-preserving learning algorithms. The project advances mathematical optimisation, machine learning, and provable safety.
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2027-CT-2
Adversarial Robustness in Deep Reinforcement Learning
Supervisor: Calvin Tsay
Description
Reinforcement-learning agents trained on financial markets are often brittle: small, adversarial shifts in market conditions or observations can quickly break a learned strategy. This project develops training methods that make deep RL policies robust under adversarial and out-of-distribution dynamics. We will draw on robust MDPs, safe/constrained RL, and worst-case perturbation analysis. The goal is to stress-test them in realistic market simulators. Building on the group's work in safe and constrained reinforcement learning, as well as in certification, you'll combine RL, robustness methods, and mathematical optimisation.
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2027-FB-1
Runtime Monitoring and Shielding to Synthesize Safe and Trustworthy RL Controllers
Supervisor: Francesco Belardinelli
Description
Reinforcement Learning has proved to be an effective method to synthesise effective controllers, including for complex tasks.
However, controllers generated through RL comes with no guarantees about their safety, compliance and trustworthiness, which in high-risk environments might lead to unintended, even harmful, consequences.
The goal of this project is to (i) build runtime monitors to check compliance of complex stochastic processes with respect to safety, security, trustworthiness requirements; (ii) integrate such monitors into a shielded RL-loop, so as to train controllers that are safe by training.
Impact
This PhD project is designed to make the following targeted contributions:
- Provide a formalisation of high-risk processes (e.g., industrial, financial, transportation) within the frame of Markov decision processes and games, also accounting for their stochasticity and uncertainty.
- Formalise relevant safety and security requirements in logic-based languages amenable to formal verification.
- Synthesise monitors automatically from the formal requirements in (2). Then deploy such monitors to verify at runtime the compliance of stochastic processes.
- Integrate the monitors into an RL-loop, where the monitors shields against dangerous actions, so as to generate controllers that are safe by training.
This project will contribute to the monitorability and safety of stochastic, high-risk processes, through the synthesis of controllers that are provably compliant and trustworthy.
Relevant references by the applicant
[1] Omar Adalat, Francesco Belardinelli: Expressive Temporal Specifications for Reward Monitoring. AAAI 2026: 19533-19541
[2] Daniel Donnelly, Francesco Belardinelli: Expressive Reward Synthesis with the Runtime Monitoring Language. PRIMA 2025: 427-434
[3] Edwin Hamel-De le Court, Francesco Belardinelli, Alexander W. Goodall: Probabilistic Shielding for Safe Reinforcement Learning. AAAI 2025: 16091-16099
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2027-AFR-1
Algorithmic and Game-Theoretic Aspects of Blockchains and Financial Markets
Supervisor: Aris Filos-Ratsikas
Description
The project aims to study the mathematical foundations that dictate the design of blockchain systems and cryptocurrencies, and more generally related financial markets characterised by volatile assets. The focus will be on the algorithmic aspects of this design (i.e., providing robust and efficient algorithmic solutions), as well as the game-theoretic aspect (i.e., making sure these solutions take the incentives of participants into account, as well as quantify and mitigate their effects).
An indicative direction is the study of stablecoin design, i.e., cryptocurrencies whose value is pegged to some real-world currency like the USD. The design of stablecoins is a fundamental task faced by many major blockchain companies today, and several different approaches have been proposed (e.g., fiat-backed stablecoins, crypto-back stablecoins, algorithmic stablecoins, etc). Yet, despite all these approaches, there seems to be a striking lack of established theory to back up and aid those designs. Concretely, one would like to systematically study questions of the type: "What is the fundamental principles that guarantee stability?", "Can stability be ensured exclusively via tuning supply and demand via providing the right user incentives?", "What are the appropriate intervention mechanisms that would facilitate those incentives" and, ultimately, "Is it even theoretically possible for a stablecoin to be both stable and long-term sustainable?"
This direction of the project would aim to develop this theory and back up the theoretical findings with corresponding experiments with real-world data. See for example https://arxiv.org/abs/2602.15981 for a first work in this direction.
Similar approaches could be applied to other problems in the blockchain/cryptocurrency domain, and more broadly to financial markets which are dictated by the same principles.
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2027-AB-1
Predictive World Models For Tabular Stock Market Data
Supervisor: Amir Bar
Description
This project explores building a predictive world model for tabular stock market data to simulate future market scenarios and evaluate trading decisions.
The goal is to learn neural representations of financial data and train a world model that predicts how market and portfolio states evolve under different trading actions.
We will use this model to plan sequences of trades that optimise risk-adjusted returns under transaction costs and portfolio constraints.
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2027-SD-1
Neuro-symbolic detection of attacks on enterprise and agentic infrastructure
Supervisor: Soteris DemetriouCo-supervisor: Francesca Toni
Description
Modern computing infrastructure, in finance and beyond, is increasingly operated and extended by AI agents that read, write and execute across many systems. This expands the attack surface in ways that existing detection tools were not designed for: supply-chain compromises can enter through model and dependency repositories, and agents themselves can be turned against their operators by adversarial inputs hidden in the data they process. Statistical detectors struggle to explain their alarms, and rule-based systems struggle to keep up with new behaviours. This project develops neuro-symbolic methods that combine the pattern-recognition strength of modern generative models with the rigour and transparency of symbolic reasoning, with the aim of detecting and localising attacks in system telemetry and agent activity while producing structured, auditable accounts of why a decision was reached. The work also studies how such detectors can be attacked, using adversarial techniques to expose weaknesses and to guide the design of more robust mechanisms. The student will work at the intersection of systems security, explainable AI and adversarial machine learning with access to established public benchmarks. The project is supervised jointly between the APSS (Applications, Systems, and Platforms Security) group and the CLArg (Computational Logic and Argumentation) group and builds on a track record of publications at top security and AI venues.
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2027-SD-2
Enforcing data-use obligations in AI-driven financial pipelines
Supervisor: Soteris Demetriou
Description
Financial organisations operate under dense contractual and regulatory obligations governing how licensed data may be used, by whom, on which systems, and for how long. As AI agents increasingly orchestrate data ingestion, feature engineering and model training, verifying that these obligations are respected end to end, including in the models trained on the data, is becoming infeasible by manual review or static access control. This project investigates neuro-symbolic techniques for turning natural-language obligations into machine-checkable constraints, monitoring AI-driven data workflows against them, and producing explanations that a compliance officer, vendor or regulator can interrogate. The student will gain expertise in security and privacy, explainable AI and applied machine learning.
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2027-CC-1
Agents for Program Reasoning
Supervisor: Cristian Cadar
Description
Software development is undergoing a profound transformation, with developers increasingly relying on AI assistants and incorporating AI-generated code. As a result, the core activity of software developers is shifting more and more from writing code to reviewing and validating it.
However, human-scale code review and validation cannot keep up with the speed and volume of AI-driven development. Therefore, automated software analysis methods—ranging from fuzzing to symbolic execution to formal verification—are becoming critical safeguards in this AI era.
To remain effective, these methods must scale along multiple dimensions: they must handle larger codebases, keep up with increasingly rapid development cycles, operate across a growing diversity of programming languages and system architectures, and infer and reason about higher-level semantic properties.
A PhD in this area would focus on addressing these challenges by devising novel agentic technique that combine traditional program analysis techniques and AI-based techniques.
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2027-TB-1
Topology-Aware Meta-Controllers for Safe and Interpretable Agentic AI
Supervisor: Tolga Birdal
Description
Agentic AI systems increasingly consist not of a single model, but of networks of interacting agents, foundation models, tools, data sources and human decision-makers. Such systems can exhibit collective behaviours that are difficult to infer from any individual component. Agents may form transient coalitions, reinforce erroneous beliefs, propagate failures, develop conflicting internal states, or produce harmful behaviours through interactions that appear benign when examined pairwise. Existing approaches to monitoring and coordinating multi-agent AI largely model these systems either as collections of individual agents or as ordinary graphs. Both representations can miss essential features of agentic systems such as the inherent higher-order interactions.
This PhD project will investigate whether Topological Deep Learning (TDL) can provide a new mathematical and computational foundation for understanding, controlling and securing agentic AI. The central idea is to represent an evolving agentic system as a higher-order structure, such as a simplicial complex, cell complex, hypergraph or sheaf, in which higher-dimensional cells encode interactions involving groups of agents, tools or information sources. Rather than observing agents independently, this representation would make the organisation of the whole system an explicit object of learning and reasoning.
The project will develop a topology-aware meta-layer operating above the individual agents. Using topological and geometric representations together with learnable TDL architectures, this layer will seek to identify emerging coordination patterns, inconsistencies and failure modes, as well as quantifying the structural state of the agent network, and, ultimately, intervening when necessary. Possible interventions include modifying communication pathways, isolating compromised components, changing task or information routing, introducing additional verification, or dynamically restructuring teams of agents.
A core research question is whether topological signatures can reveal emergent failures before they become visible through conventional agent-level metrics. Persistent and dynamic topological summaries, higher-order message passing, Hodge-theoretic representations and sheaf-based consistency models will be investigated as mechanisms for detecting phenomena such as cascading errors, adversarial or compromised agents, unstable feedback loops, groupthink, anomalous coalitions and inconsistent information flows. These representations will also be explored as a route to interpretability: instead of merely assigning a scalar risk score to an agentic system, the meta-layer will expose which interaction structures changed, where inconsistencies arose, and how a failure propagated through the system.
The project will combine theory and algorithm development with controlled experiments on multi-agent systems based on language models and reinforcement-learning agents. Particular emphasis will be placed on robustness under distribution shift and adversarial behaviour, stability of learned topological representations, scalability to large dynamic agent networks, and intervention-based validation of proposed explanations. An ambitious longer-term goal is to establish conditions under which structural properties of the higher-order interaction network imply guarantees on system-level stability, consistency or containment of failures.
Financial computing provides a particularly demanding test environment for these ideas. Multi-agent systems used for research, simulation, monitoring, risk analysis or distributed decision support must operate under uncertainty while remaining robust, auditable and resilient to faults. The resulting methods, however, would be broadly applicable to agentic AI systems in other high-stakes domains.
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2027-TB-2
Learning the Higher-Order Topology of Dynamic Financial Markets
Supervisor: Tolga Birdal
Description
Financial markets are complex adaptive systems in which assets, sectors, institutions and information sources interact across multiple spatial and temporal scales. Most quantitative representations of these dependencies are nevertheless fundamentally pairwise: correlation matrices, covariance networks, graphical models and conventional graph neural networks describe relationships between pairs of entities. Yet many economically meaningful phenomena are intrinsically collective. Market regimes, sector rotations, contagion, coordinated responses to macroeconomic shocks and transient arbitrage relationships may arise through interactions among groups of assets that cannot be adequately reduced to a collection of pairwise dependencies.
This PhD will develop a new framework for discovering, representing and learning the higher-order structure of dynamic financial markets using Topological Deep Learning (TDL). Rather than assuming that the relevant market network is known in advance, the project will investigate how latent higher-order interactions can be inferred directly from multivariate financial data and represented through structures such as simplicial complexes, cell complexes and hypergraphs. These structures provide a natural mathematical language for encoding interactions among multiple assets simultaneously and for distinguishing genuinely collective effects from combinations of pairwise relationships.
A central challenge will be that the topology of a market is neither directly observed nor stationary. The project will therefore develop methods for jointly learning market topology and predictive representations through time. Higher-order structures may be inferred from price and return dynamics, volatility, trading activity, cross-asset signals and other multimodal information, with their evolution modelled as a dynamic topological system. Topological Deep Learning architectures will then operate on these learned structures, allowing information to propagate not only between individual assets but across higher-order relationships involving groups, sectors and potentially multiple asset classes.
The project will investigate whether these representations reveal latent market organisation that is inaccessible to conventional graph-based approaches. For example, topological features may identify the formation or dissolution of tightly interacting groups of assets, changes in the dimensionality or connectivity of market structure, or the emergence of abnormal higher-order dependencies preceding periods of instability. Tools from persistent topology, Hodge theory, higher-order message passing and topological signal processing will be explored alongside learnable neural architectures.
A major research direction will be dynamic topology discovery. Instead of constructing a market graph using a fixed similarity measure or threshold, the goal will be to learn which interactions are relevant for a downstream task while preserving meaningful structural constraints. This raises fundamental questions at the intersection of machine learning and topology: when is a higher-order relation statistically identifiable? How should topology be regularised across time? Which topological features are stable under noisy observations? And when does modelling interactions beyond pairs provide genuinely new predictive information?
The learned representations will be evaluated across tasks such as market regime identification, cross-asset forecasting, anomaly and instability detection, risk propagation and out-of-distribution generalisation. Particular attention will be given to periods of structural change, where models based on historical pairwise relationships may fail. Rather than treating these shifts purely as distributional anomalies, the project will investigate whether they can be understood as changes in the topology of the underlying interaction system.
Interpretability will be a core objective. Because higher-order cells and topological features correspond to explicit structures within the market, the resulting models offer the possibility of explaining predictions through changes in the organisation of interacting assets rather than solely through latent neural representations. The project will investigate methods for attributing model behaviour to particular higher-order interactions and for visualising how learned market structure evolves across regimes.
The overarching goal is to establish a framework in which financial markets are treated not as fixed graphs but as evolving higher-order systems whose latent topology can be discovered from data. Beyond improving particular predictive tasks, the project aims to answer a more fundamental question: what structure does a machine-learning system discover when it is allowed to learn the geometry and topology of a market rather than having that structure imposed in advance?
The resulting methods could provide new tools for analysing complex financial systems while contributing more broadly to Topological and Geometric Deep Learning for dynamic, noisy and partially observed environments.
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2027-TB-3
Learning the Geometry of Financial Markets: Riemannian Machine Learning and Optimisation
Supervisor: Tolga Birdal
Description
Many of the mathematical objects underlying modern quantitative finance are inherently non-Euclidean. Covariance and correlation matrices lie on manifolds of symmetric positive-definite matrices, factor models and dynamic subspaces naturally inhabit Grassmann and Stiefel manifolds, probability distributions admit information-geometric representations, and constrained portfolios, volatility structures and latent market states often possess geometric structure that is lost when they are represented in ordinary Euclidean coordinates.
At the same time, much of contemporary machine learning and numerical optimisation treats these objects as unconstrained vectors in a flat parameter space. This can lead to inefficient optimisation, unstable learning, poor extrapolation and models that fail to respect the intrinsic structure of the quantities being learned.
This PhD will investigate a different paradigm: can the geometry of financial models and financial data be exploited, and in some cases learned—to obtain more efficient, stable and interpretable machine-learning and optimisation methods?
The project will develop methods at the intersection of Riemannian geometry, machine learning, optimisation and quantitative finance. A central focus will be the design of geometry-aware learning algorithms in which optimisation takes place directly on the appropriate manifold rather than through an unconstrained Euclidean parameterisation. Candidate geometries include the manifold of symmetric positive-definite matrices, Grassmann and Stiefel manifolds, product manifolds arising from structured financial models, and information-geometric spaces of probability distributions.
One research direction will investigate Riemannian optimisation for dynamic covariance, factor and risk models. Financial dependence structures are high-dimensional, noisy and time-varying, yet their mathematical representations possess strong geometric constraints. The project will study whether geodesic interpolation, intrinsic regularisation, Riemannian gradient methods and manifold-valued dynamical models can improve the estimation and tracking of these structures, particularly during periods of regime change or market stress.
A second direction will explore Riemannian machine learning for financial prediction and representation learning. Instead of first embedding structured financial objects into Euclidean space, models could operate directly on manifold-valued inputs or latent states. This may include geometry-aware neural architectures, Riemannian recurrent or state-space models, and manifold-valued latent representations for evolving market states. Applications could include regime identification, volatility and risk forecasting, cross-asset modelling and anomaly detection.
A particularly ambitious component of the project will ask whether the relevant latent geometry itself can be learned from data. Classical Riemannian methods assume that a metric is specified in advance. In a financial system, however, the geometry that best captures economically meaningful similarity or sensitivity may change through time. The project will therefore investigate adaptive or learned Riemannian metrics that reflect the local structure of market dynamics and simultaneously improve downstream optimisation.
This creates a close connection between learning and optimisation, determining which perturbations are small, which directions are important, and how optimisation trajectories evolve. The project will investigate whether such learned geometries can act as task-dependent preconditioners, producing faster and more stable optimisation while retaining an interpretable relationship to financial structure.
The theoretical component will study questions of convergence, stability and generalisation on curved parameter spaces. This may include analysis of Riemannian stochastic gradient methods, natural-gradient-like algorithms, geodesic convexity, adaptive metrics, and the interaction between manifold curvature and the conditioning of high-dimensional financial optimisation problems. Where appropriate, the project will seek guarantees concerning convergence rates, robustness to noisy observations and stability under changes in market regime.
Various financial applications will provide demanding test cases in which structural constraints and non-stationarity are unavoidable. Potential problems include dynamic covariance estimation, portfolio and risk optimisation, latent factor tracking, volatility modelling, market-regime identification and uncertainty quantification. The objective is not simply to apply existing manifold algorithms to finance, but to use financial problems to motivate new methods in Riemannian machine learning and optimisation.
The broader goal of the PhD is to establish a principled framework for geometry-aware learning in dynamic, high-dimensional systems, addressing a fundamental question: when the objects being learned are intrinsically curved, how much can be gained by allowing the learning and optimisation algorithms to respect—and ultimately discover—that geometry?
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2027-AD-1
Formally Verified LLM Inference
Supervisor: Alastair DonaldsonCo-supervisor: Marios Kogias
Description
LLM inference engines are critical infrastructure on which societies around the world depend. Cyber attacks on LLM infrastructure have the potential to deny access to critical services, compromise privacy and isolation between tenants in data centres, and form the basis of remote execution attacks. This PhD project will focus on the design of secure-by-construction LLM inference engines using formal methods, through the Lean proof assistant. It would be ideal for a student who is interested in (a) how inference works at the systems level (including how to work with highly optimised GPU kernels and multi GPU setups in a distributed environment), (b) using formal methods at scale, and (c) leveraging generative AI to apply proof assistants effectively in this setting.
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2027-RB-1
Quantum Computing for Learning Under Uncertainty
Supervisor: Roberto Bondesan
Description
Can quantum computers find better solutions in the complex optimisation landscapes that arise when learning from noisy data? This PhD project will explore how quantum dynamics can navigate nonconvex objectives, building on emerging connections between quantum mechanics, stochastic processes, and optimisation. A central challenge is to understand when quantum advantages survive the uncertainty, interactions, and computational costs encountered in realistic learning problems. The research will combine mathematical analysis, quantum algorithm design, and numerical experiments, with potential applications to financial model calibration and nonlinear time-series learning within QRT Labs. By comparing quantum approaches with powerful classical methods, the project aims to establish when quantum computation can deliver reliable solutions more efficiently and how to design algorithms that exploit those opportunities. It offers an exciting opportunity for students interested in quantum computing, applied mathematics, and machine learning to work at the interface of fundamental theory and practical challenges.
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2027-HF-1
Privacy-Aware Heterogeneous Edge-to-Core System for Financial Applications
Supervisor: Hongxiang Fan
Description
The rapid adoption of AI in financial computing is increasing the demand for more capable models, while also placing greater pressure on latency, scalability, and the secure handling of sensitive data. Financial workloads are becoming increasingly heterogeneous, often requiring different forms of market, transaction, and institutional data to be analysed together rather than by a single model or computing environment. This project therefore investigates how machine learning can be co-designed with distributed systems to support scalable, efficient, and privacy-aware heterogeneous financial computing.
Many financial applications require information from multiple data sources and computational environments to be combined in order to support timely and accurate decision-making. Examples include market analysis, risk assessment, transaction analytics, and other data-intensive financial services. Processing such workloads across local and central systems creates an important trade-off: filtering or compressing data can reduce communication and computational overhead, but may also remove information that is important for downstream analysis. Transmitting detailed data to central systems can increase resource consumption and expose sensitive financial or proprietary information. This challenge becomes even more prominent with large language models (LLMs), whose heavy computational and memory requirements and large input contexts can significantly amplify communication costs and privacy risks in distributed deployments. This raises the question of how specialised models should be distributed across the computing hierarchy and what information should be exchanged between them.
Building on our prior work on efficient multi-model inference, such as edge infrastracture for LLM test-time scaling, this project aims to develop a privacy-aware heterogeneous edge-to-core framework for financial applications. The framework will determine where specialised models should execute and how intermediate information should be exchanged between local and central components. It will explore adaptive mechanisms for retaining task-relevant information while reducing unnecessary transmission and exposure of sensitive data. Its effectiveness will be assessed against local-only, centralised, and fixed-partition systems, considering both application-level performance and system-level costs such as latency, communication overhead, resource utilisation, scalability, and information leakage.
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2027-DP-1
Safe Learning and Control Out of Distribution
Supervisor: Dario Paccagnan
Description
Modern AI and control systems are trained on finite data, yet they are deployed in environments that rarely behave exactly like the data used for training. Distribution shifts may arise from changing operating conditions, modelling errors, sensor biases, new environments, or interactions between a controller and the system it controls.
This PhD will develop new methods for safe learning and control under distribution shift, with the goal of providing rigorous guarantees on the behaviour of learning-enabled systems when deployment differs from training. The project will combine ideas from machine learning, optimisation, control theory, statistical learning and formal verification.
Research questions will include how to certify safety from finite data, how to exploit physical and temporal structure in distribution shifts, and how to design controllers that remain reliable beyond the observed training distribution. The work will span fundamental theory, new algorithms, and applications to learning-enabled dynamical systems.
The project is particularly suited to students interested in the mathematical foundations of reliable AI, safe machine learning, optimisation, or data-driven control.
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2027-PP-1
Economics-Informed Deep Reinforcement Learning for Robust, Explainable Decisions under Uncertainty
Supervisor: Panos ParpasCo-supervisor: Alexander Michaelides
Description
Many problems in economics and finance (saving and investment over a lifetime, asset pricing, market making, monetary and fiscal policy) are sequential decisions under uncertainty.
Deep reinforcement learning (RL) can learn decision rules for such problems when they are too complex for classical methods, but it ignores what economic theory has already established about the answer: monotonicity and concavity of value and policy functions, budget feasibility, no-arbitrage. Inspired by physics-informed neural networks, this project will develop economics-informed deep RL, in which such restrictions are built into the neural architecture, the training objective and the diagnostics.
Recent work by the supervisory team shows that neural policies with near-optimal average performance can still behave in economically impossible ways, and that imposing structure removes these errors while improving sample efficiency.
The project will attempt to provide answers to the following open questions.
- Which economic restrictions can be enforced exactly within deep RL, and how do they affect stability, sample efficiency and the compounding of errors over long horizons?
- How should policies be trained when parameters are estimated, data are limited and conditions change, drawing on robust RL and the economics of ambiguity?
- How can sensitivity analysis, counterfactual explanations and solution-free diagnostics let users change assumptions and see which conclusions survive?
The methods will first be tested on problems with known solutions, where their accuracy can be measured exactly, and then extended to higher-dimensional and more complicated models for which no solution is known and where the economic restrictions and diagnostics become the only available check. To the extent that they overcome the curse of dimensionality, this opens up richer portfolio choice problems with many assets, income sources and frictions, studied for different actors in the economy (households, corporates, pension and sovereign wealth funds) from both a normative angle (what should an agent do?) and a positive one (does the model explain what agents actually do?). This provides a quantitative laboratory for understanding risk and return trade-offs under realistic uncertainty. The resulting models will be made available through an interface (currently the Model Context Protocol) through which other AI systems can configure, solve and interrogate them while preserving restrictions, communicating uncertainty and flagging when a change invalidates a previous guarantee.