Papers

Large language models (LLMs) are increasingly used in investment decision-making, yet prior work shows that they exhibit systematic, model-specific investment preferences. We study whether a model's overall investment stance can be calibrated to a specified direction and strength. We introduce an investment-bias dial, an inference-time intervention on a single neuron that continuously adjusts a model-level decision prior—its overall tendency toward buying or selling—without targeting specific firms or investment attributes. Using matched positive and negative evidence, we evaluate five open-weight LLMs and find that the dial produces monotonic changes in investment stance without modifying prompts or model parameters. At the response level, the dial shifts both investment decisions and the evidential emphasis of generated rationales under identical inputs. In an agentic retrieval setting, the dial also changes what information the model searches for, which evidence it selects, and which evidence is reflected in its final analysis. In a long-context evaluation, the dial maintains stable stance control as context length increases, whereas a matched system-prompt instruction progressively attenuates. We further show that changes in the dial propagate to security rankings and downstream portfolio composition in an exploratory backtest. Overall, our results show that an LLM's aggregate investment stance can be calibrated toward a specified target at inference time.

The stability of markets hosting leveraged exchange-traded products is governed not by any single product's loop gain but by the spectral radius of a loop-gain matrix, and scalar per-product monitoring underestimates system feedback by construction. Recent work measures the self-reinforcement of a leveraged fund's daily close rebalancing through a scalar loop gain and treats cross-asset spillovers as bias. We model complexes on correlated underlyings as a coupled feedback system with matrix gain L and show that scalar monitoring has two blind spots: (i) cycle amplification, since rho(L) >= max_i l_ii for nonnegative coupling, strict under two-way coupling; and (ii) transmitted displacement, which arises already under one-way coupling and is invisible to the receiver's own gain. We give a reduced-form estimator of L requiring only prices and public fund assets – no signed order flow – via cross-asset overnight reversals, reporting its measurement-convention sensitivity explicitly. In simulation the spectral radius is recovered with RMSE 0.005 at T=250, a lead-lag confounder yields a 2% false-alarm rate, and in a calibrated blind-spot configuration the scalar monitor reports "safe" and the matrix monitor "unsafe" on 100% of paths. In the 2026 Korean single-stock LETF episode we detect transmission from the SK Hynix complex into Samsung Electronics' closing price (DiD z=-2.82; exact randomization p=0.0055 against 182 control pairs), scaling with the sender's rebalancing capital; conservatively, about 41% of Samsung's closing displacement variance is imported – invisible to its own "moderate" gain of 0.24. The same estimator returns nulls for the U.S. MSTR-Bitcoin-Coinbase complex, whose capital is comparable but whose closing venue is far deeper. Monitoring should be organized around the (complex x venue) matrix, not around products.

A companion paper \cite{ItkinDF2026} introduced the Diagonal Frog (DF) positivity-preserving schemes for anisotropic Fokker–Planck equations, advancing each directional substep by a Krylov-computed matrix exponential, which dominates the cost. Replacing that exponential by a rational map $r(\gamma L)$ reduces the substep to a banded solve, but the positivity argument no longer applies. We prove that for eventually exponentially positive generators the entrywise sign of $r(\gamma L)$ at large steps is decided by a single number, the value $r(\infty)$ taken on infinitely stiff modes. Nonnegativity holds above a computable threshold when $0\le r(\infty)<1$, and at most on a bounded interval, empty or vanishingly narrow in all our tests, when $r(\infty)<0$. The criterion rejects the Crank–Nicolson (trapezoidal) method, where $r(\infty)=-1$, and selects the subdiagonal Padé$(0,2)$ method, which is second order, L-stable and provably positive above an explicit threshold. The resulting DF-ADI scheme costs $O(N)$ per step, keeps the implicit factorized mixed derivative unchanged, is second order in space and time, and conserves discrete mass exactly. In the strong cross-diffusion regime, however, the directional factors demand a step larger than the mixed derivative permits, so the composite second-order scheme is only empirically positive there, and the criterion serves to discriminate the well-behaved multiplicative factors from the stabilizing-correction schemes rather than to guarantee positivity. Against the Krylov exponential it runs ten to thirty-two times faster at matched accuracy in our tests with the gain growing with the mesh. We extend the construction to the backward Kolmogorov equation and to jump-diffusion models.

When shopping is delegated to AI agents, it is unclear whether the ranking advantage documented for humans persists. Across 7,000 sessions with five large language models (LLMs) and varying reasoning effort, we compare AI agents with human field data. AI agents search more extensively than human consumers. As with humans, lower-ranked listings are less likely to be inspected, although the effect is smaller for AI agents. Unlike humans, AI agents show a pattern consistent with the lost-in-the-middle effect, whereby middle listings have the lowest probability of inspection. At the choice stage, position effects are concentrated at lower reasoning effort, but higher effort reduces the middle penalty for every LLM that exhibits it. These findings suggest that, when search is delegated, displayed attributes may matter more than placement, and that exposure to position bias depends on how the AI agent is configured.

Financial stability rests on the premise that distress is largely idiosyncratic and therefore diversifiable: when one institution errs, the rest of the system absorbs the shock. That premise fails when many decision-makers depend on the same infrastructure. Agentic AI systems, which take consequential actions rather than only emitting predictions, are becoming such a substrate, and the binding concern shifts from the model risk of a single deployment to the systemic risk of the population. We develop this account in six mathematical settings. Chapter 1 recasts the PD/LGD/EAD decomposition of expected loss as an expected-harm identity and introduces a set-valued containment-risk measure; under a lever-assignment axiom that review cannot intercept an irreversible action, no non-preventive control satisfies a coherent tail constraint. Chapter 2 lifts this to a fleet sharing a foundation model: the shared model is a non-diversifiable common exposure whose expected-shortfall floor holds however large the fleet grows, and a percolation threshold governs contagion. Chapter 3 recasts these dynamics as a marked, Hawkes-excited jump diffusion, identifying the robust stress problem with a time-consistent entropic risk measure. Chapter 4 treats runtime guardrails as partially observed stochastic control, giving an observability trichotomy, a detection floor, and, under commit exogeneity, a runtime-impossibility corollary. Chapter 5 makes the adversary a player, yielding an underinvestment wedge proportional to systemic reach. Chapter 6 makes capability a state variable in an arms race. One claim runs through all six: the systematic component of agentic risk cannot be diversified, detected away, or reversed, and only ex-ante structural prevention moves it.

This paper asks whether firms' exposures to news about different types of AI risk are priced in U.S. stock returns. Using AI and risk keywords, I identify 7,787 Wall Street Journal articles from January 2016 to December 2025. I combine latent Dirichlet allocation (LDA) with the Domain Taxonomy in the MIT AI Risk Repository to construct four news-based systematic risk factors. I estimate betas to factor innovations and test pricing with univariate portfolio analysis and Fama-MacBeth regressions. Only the taxonomy-mapped Misinformation factor (D3) is robustly priced. Its high-minus-low beta portfolio earns monthly alphas of 0.49%-0.57%, and the estimated D3 price of risk is positive and statistically significant across beta-estimation windows, conventional factor and industry controls, alternative innovation models, and the pre-ChatGPT subsample. The other factors are not reliably priced, indicating that AI-risk pricing is domain-specific.

W-shaped smiles appear in near-expiry options around binary events such as earnings, and have been associated with bimodal risk-neutral densities. The three-parameter eSSVI slice cannot produce them. This paper defines WSVI, a parametric family for implied volatility that admits negative at-the-forward curvature and bimodal implied densities, and develops its static no-arbitrage structure. The construction factorizes total variance into a level and a dimensionless shape of normalized log-moneyness. The shape extends the per-slice eSSVI form with bounded one-sided basis terms, which add flexibility in the interior while leaving the leading-order wing behavior controlled by the affine and quadratic components. We characterize the family's exact domain and write the butterfly, vertical spread, and calendar conditions directly in shape coordinates.

Complex systems are often organised into hierarchies whose internal interactions are stronger or faster than interactions across levels. When markets are treated as genuinely multilevel systems it becomes natural to represent them as systems with hierarchical causality. Here we show that reflexivity can be formulated within such a discrete hierarchical causal system; but one in which a higher-level actor state restricts the lower-level transition kernels that remain admissible. Then event dynamics can be separated from calendar embeddings: a set-valued actor-conditioned correspondence can be used to define the admissible family of event kernels, while joint state and waiting-time laws can be used to determine compatible timing to then natural demonstrate reflexivity. A selected event-state law need not determine a unique calendar embedding. Locally, uniqueness of the joint event or timing specification requires uniqueness of both the admissible event kernel and its compatible timing law. Reflexivity is thus the endogenous closure of a hierarchical constraint loop, while timing and projection can generate calendar-time memory or causal ambiguity even for Markov event dynamics.

Implied volatility surfaces summarise the option market and are central to many financial applications. Forecasting their future evolution requires modelling two-dimensional geometry, temporal dependence, and predictive uncertainty while preserving economic admissibility. We propose a conditional latent diffusion framework for generating joint 30-step trajectories of implied volatility surfaces and underlying returns. An arbitrage-aware autoencoder learns a low-dimensional surface representation, while the diffusion model captures the conditional joint evolution. Evaluated on SPX surfaces, the framework generates realistic probabilistic multi-step scenarios while also outperforming the persistence benchmark in point forecasting.

At 15-minute horizons, directional mean reversion is far stronger and more pervasive in cryptocurrency markets than in US equities: scored under one matched, strictly out-of-sample protocol, 90% of 183 Binance pairs carry significant directional reversal against 2.7% of 187 US stocks and ETFs, in every focal coin-year since 2021. The signal lives in signs, not magnitudes: lag-one return autocorrelation is near zero on the major coins, yet simply betting against the previous candle captures most of the effect. US-listed funds whose net asset value is a crypto or metal price inherit their underlying's reversal, including its absence, from their first months of trading; stocks merely correlated with the same underlyings inherit nothing: descriptive evidence that a wrapper's tape reads like the process it wraps, not the venue it prints on. On the originating tape, the reversal concentrates after moves driven by aggressive taker flow and grows with flow intensity, while the order-book depth a move consumes conditions nothing: a conditioning consistent with compensated liquidity provision, not a test that selects it. The gross edge peaks near 1.3 bp per trade against a 5 bp round-trip cost: large enough to detect, too small to clear benchmark spot capture costs. The contrast survives an artifact battery, an exact permutation null, and a frozen six-month holdout, with a class-mean AUC gap of +0.031 as designed and +0.011 (95% CI [+0.008, +0.014]) under the most conservative accounting, clear of zero either way.

We study discrete-time asset pricing with bid-ask spreads and model uncertainty. The family of probability measures enters the no-arbitrage condition through the union of its supports. In the single-period setting, we establish fundamental theorems of asset pricing with and without short-sale constraints. In the unconstrained market, no arbitrage is equivalent to the existence of a full-support martingale consistent price system. Under short-sale constraints, the martingale condition is replaced by a supermartingale condition. We then extend these results to a finite multi-period tree. The initial information is allowed to be nontrivial, so the initial trading cost and valuation bounds may depend on the initial state, and the corresponding inequalities are formulated conditionally. Finally, for a family of pricing measures, we introduce lower and upper robust supermartingale consistent price systems. We show that no arbitrage implies the existence of a lower system, while the existence of an upper system is sufficient for no arbitrage. A two-state example shows that the lower condition alone is not sufficient.

In 2025, bilateral foreign aid was reduced by 23%, affecting more than 130 aid recipient countries. We assess whether debt service relief or remittance increases can match the USD 26 billion in aid losses. Using a network-shock model calibrated to bilateral donors' individual cuts, we estimate recipient-country aid losses and evaluate compensation feasibility in terms of annual debt service payments that would need to be cancelled and remittance capacity (the headroom between flows and a theoretical maximum in which every working-age migrant sends funds) mobilised to financially offset them. We find that 18% external debt service relief and 10% of remittance mobilisation could compensate half of the affected countries. However, some countries remain locked out of either or both mechanisms. A fundamental trade-off in the global financial architecture emerged for large aid-cut losers: countries positioned to benefit from debt service relief lack large international diaspora networks (limiting their capacity to increase remittances), while those with established diaspora channels face structural exclusion of traditional debt markets, rendering debt service relief ineffective. These insights introduce nuance in how alternative finance sources can replace foreign aid.

Option-implied rates are often treated as frictionless because completed boxes deliver riskless payoffs. I show that this interpretation requires option- and benchmark-side implementation wedges to offset. Using SPX and RUT options from 2012-2025, I find a 2-3 bp unannualized increase in the option funding basis when maturity first crosses December 31. The effect behaves as a fixed price wedge, strengthens in the mid-2010s, survives alternative contracts and benchmarks, appears independently in government-bond CIP, and is reproduced in an independently constructed option panel. Put-call parity can identify discount rates precisely without establishing their economic purity.

In online product search, returned alternatives often look alike. We investigate when a product's visual separation from its closest look-alike in a returned set increases its choice probability. We introduce two occasion-level constructs: contextual visual distinctiveness (image distance from the nearest similar alternative in the consideration set) and relative fit (compatibility with the search query). We hypothesize that distinctiveness favors selection and is highly contextual, yields a premium that rises with relative fit, and matters most when text descriptions fail to differentiate options. Analyzing over 800,000 e-commerce search events using dense representations, we apply search-event and product fixed effects to evaluate the exact same product alongside varying visual neighbors. Results show a product is significantly more likely to be clicked when it lacks a close look-alike. This distinctiveness premium increases with relative fit and roughly doubles when competing descriptions are highly similar. Consistent with a model where distinctiveness aids in standing out pre-evaluation rather than increasing inherent utility, the extra clicks distinctiveness recruits convert 5-7% less often downstream. Ultimately, the evidence characterizes visual differentiation as a local attention allocation mechanism whose value depends on query fit and information from competing cues.

Emile Durkheim's Suicide: A Study in Sociology (1897) predates much of the statistical machinery that quantitative modellers now take for granted. Yet, working with sparse and imperfect observational data, Durkheim repeatedly arrives at practices that remain remarkably relevant to modern modelling. This paper revisits Suicide from the perspective of quantitative risk modelling, not for its substantive conclusions, but for the reasoning by which Durkheim reached them. His approach illustrates how careful definition, common sense, logical investigation, scepticism toward convenient explanations, and close attention to what the data can and cannot support—all of which must precede, and can often substitute for, statistical sophistication. The broader lesson is simple: good modelling begins not with technique, but with understanding the problem, interrogating the evidence, and reasoning carefully about what it can actually tell us.

Basket options are difficult to value under correlated lognormal dynamics because weighted sums and differences of lognormal variables have no tractable distribution. This paper develops a probability-based four-moment framework that separates the exact pricing representation from the distributional approximation. A change of measure first writes a basket price as a linear combination of probabilities. For a standard basket with one positive weight, these probabilities become CDF values of positive correlated lognormal sums. Each sum is approximated by a shifted lognormal variance mixture matched to its first four moments. For an unrestricted mixed-sign basket, a signed shifted lognormal proxy gives an analytical call-price formula. We state admissibility conditions, provide a practical root-selection rule, establish the main strike-based financial properties of the direct proxy, and derive exact pricing-error identities in terms of cumulative distribution function (CDF) discrepancies. The numerical analysis combines standard-basket benchmarks with an empirical application to a normalized $3{:}2{:}1$ crack spread constructed from RBOB gasoline, ULSD or heating oil, and WTI futures. The results show that the probability reformulation and the fourth-moment condition improve the distributional fit and pricing accuracy, particularly when maturity and tail asymmetry increase. The framework remains analytical, transparent, and suitable for repeated valuation across strikes and maturities.

We study an experiment with 8.5 million users on Netflix's recommender system to measure how improvements in recommendation technology affect the set of products that get consumed. Improvements increase total consumption and users' reliance on recommendations while diffusing recommendations and consumption away from the most popular titles (“superstars") toward a larger number of moderately popular titles (“middle-tail"), with minimal effects on the most niche titles (“long-tail"). Our results challenge the notion that recommender systems polarize consumption – raising the consumption shares of the head and tail at the expense of the middle – and suggest that the returns to investing in middle-tail products grow as algorithms improve and platforms scale.

Marketing Mix Models (MMMs) estimate the incremental sales effect of advertising from observational time series, yet they are rarely validated against ground truth, because ground truth is unobservable in real data. Synthetic data closes that gap in principle, but existing generators produce marketing spend exogenously - omitting the central difficulty of the estimation problem, since real budgets are planned around promotional calendars, seasons, and recent performance. This paper presents a parameterized generator, and a fixed reference instance, of a synthetic weekly retail dataset (156 weeks, three media channels) in which spend arises from four documented coordination mechanisms - quarterly budget feedback, anticipatory spending ahead of a promotional calendar, scheduled TV bursts, and algorithmic performance chasing - on a demand baseline with seasonal, quality, price, and unobserved sentiment components. Spend translates into incremental sales through two transformations, carryover and diminishing returns, instantiated here as geometric adstock and logistic saturation with known parameters; the true causal decomposition of every week's sales is recorded alongside the error-contaminated variables a practitioner would observe. Every mechanism is a parameter that can be varied or switched off, and a companion procedure simulates go-dark geo-experiments with exact treatment effects. The seeded generator and reference instance are publicly released with notebooks that reproduce every number in this paper.

Marketing Mix Models (MMMs) are widely used for marketing measurement and budget allocation, but face fundamental identification challenges: due to endogenous marketing spend decisions, MMM estimation on observational time-series data cannot recover the true causal effects of marketing. On the other hand, geo-experiments provide causal identification through randomization, but it is not clear how to use them efficiently to calibrate marketing mix models. We propose a novel structural estimation approach that recovers the complete set of MMM parameters - adstock decay ($\alpha$), saturation ($\lambda$), and effectiveness ($\beta$) - directly from geo-experimental time-series. By differencing outcomes between treatment and control regions, our method eliminates observed and unobserved confounding factors while preserving the temporal variation that identifies each parameter. We demonstrate on synthetic data that this approach recovers the true ROAS and the response curve over the range of spending covered by the experiments, together with credible estimates of the underlying parameters. Our framework enables efficient pooling across multiple experiments and provides a principled foundation for MMM calibration that fully utilizes the information experiments contain.

Deep hedging is a data-driven approach to learn hedging strategies. It relies on synthetic price paths generator, as real market data is often limited for training. Existing approaches primarily evaluate such generators based on realism, i.e., how well they capture statistical properties of real markets, but the relationship between realism and hedging performance remains unclear. In this work, we introduce a decision-centric perspective on synthetic data for deep hedging based on the notion of compatibility. Compatibility measures the extent to which strategies trained on synthetic scenarios remain effective in the true market. We theoretically show that 1) hedging performance decomposes into learning error and a compatibility gap, and 2) realism and compatibility can diverge. Empirically, we find that hedging performance is governed not by realism alone, but by the alignment between the generator and the hedger, together with task structure. Taken together, this work provides a principled basis for designing synthetic data in finance aligned with decision tasks.

Tests of conditional mean independence can lose power when departures are confined to a bounded part of a multivariate predictor space and the relevant spatial scale is unknown. We propose a Multiscale Ball Conditional Mean Independence (MBCMI) test that aggregates support-weighted local mean contrasts in an outcome variable across balls centered on each data point in a predictor set. Fixed-grid theory identifies the population target, establishes consistency for grid-visible alternatives, and derives a Pitman local-power limit governed by the ball-smoothed mean departure. For serial data, feasible recursive-sign-bootstrap validity for stable finite-order autoregressions with conditionally sign-symmetric innovations is established. Application-aligned serial null experiments reject 4.25% of the time. MBCI is demonstrated to be strongest for local and radial signals. Predictor-law experiments show that these conclusions are not an artefact of independent Gaussian covariates. In monthly U.S. finance data, cross-fitted residual MBCMI tests remove every full-sample rejection, suggesting contemporaneous conditional-mean dependence rather than evidence of distinctive nonlinear structure.

We study, theoretically and experimentally, how transparency about students' priorities and admission chances shapes their incentives to acquire information about their own preferences in school choice and college admissions. In the model, uninformed students choose schools based on a common prior. When they learn their own preferences, their choices become more heterogeneous, which frees up seats at popular schools. Students who know they have high priority have stronger incentives to learn because they can more readily act on what they learn, whereas students who know they have low priority are discouraged. Full priority disclosure concentrates learning among high-priority students. By pooling priorities, partial disclosure spreads learning incentives to pooled students and yields higher welfare. In the laboratory, however, full disclosure yields the highest welfare instead, followed by partial disclosure, and then no disclosure, because greater transparency improves subjects' understanding of the strategic environment, leading to fewer mistakes. These findings support full disclosure of priorities or admission chances to guide information acquisition. However, deviations in learning remain even under greater priority transparency, partly because subjects respond suboptimally to admission chances when these are provided directly rather than inferred. Students' ability to interpret and use them is therefore itself a policy concern.

The Marketron model of \cite{HalperinItkin2025Mark} and its option pricing extension in \cite{HalperinItkinMarketron2} suffer from structural non-identifiability: an eighteen-parameter space traps solvers in suboptimal local minima and renders economic quantities unmeasurable. By removing exact scaling gauges and sign symmetries, freezing non-financial parameters by explicit criteria, and adiabatically eliminating the fast hidden signal, we derive a robust nine-parameter reduced model. A Gauss-Newton Hessian with empty null space and a manifold-boundary analysis confirm that the reduced core carries no exact symmetry and admits no further reduction. A diffusive correlation between flow and return innovations captures the short-maturity skew. A staged calibration from the physical measure to the risk-neutral measure, illustrated on SPX options, fits the whole surface with a single parameter set. The same reduction turns the wedge between the physical and pricing values of the flow block into a well-defined market price of flow risk rather than a ridge artifact, identifiable here for the first time, though a single surface constrains its level only weakly. Finally, our analysis reveals that in the Marketron model the log-price obeys a generalized Langevin equation with a closed-form, state-modulated memory kernel, and that the memory variable itself is the exact Markovian lift of this kernel. This mapping also yields a testable condition, the equality of the signal and memory relaxation rates, which on the SPX surface come out well separated, though both weakly identified, placing the fitted market tentatively in the driven, non-equilibrium regime and turning the active-matter reading from an analogy into a falsifiable constraint.

Costly LLM features matter only if calibration lets them affect the forecast. We document a failure of this link in a next-day risk study of two broad-market funds. Full-history scoring preceded the 2022 calibration. Calibration then set all four LLM weights to zero. The 856 later scores therefore could not affect the evaluation. We call this calibration-induced degeneracy. Allowing signed weights reactivated all four mappings. None improved forecasts after familywise correction. By contrast, a near-zero-cost headline count reduced SPY variance-forecast loss by 0.001720 (95 percent familywise interval: [0.000719, 0.002830]). The cheap baseline is therefore a critical diagnostic. We propose a calibration-viability checkpoint. Fit the mapping, perturb the feature over prespecified calibration values, and require a meaningful forecast response before acquiring holdout features. The check uses no holdout outcomes. Here, it would have stopped the paid full-history inference phase.

We study continuous-time dynamic portfolio optimization under a Conditional Value-at-Risk (CVaR) constraint on the investor's terminal loss. For a general class of convex trading objectives, we exploit the auxiliary-threshold representation of CVaR to establish the existence of an optimal strategy and strong duality without requiring market completeness. These results motivate a dual-based nested bisection–golden-search algorithm over the threshold and Lagrangian multiplier, where the inner iterations reduce to standard unconstrained stochastic control problems. We prove that the resulting strategies converge to the optimal control as the number of iterations tends to infinity. Numerical experiments recover the Merton policy when the risk constraint is nonbinding. When the constraint is binding, the optimal strategy becomes state dependent: the investor reduces risky exposure following adverse outcomes but preserves, and near maturity may increase, exposure following favorable outcomes. Thus, a terminal CVaR constraint produces an asymmetric reallocation across states rather than uniform de-risking. Nontraded endowment risk amplifies the conservative adjustment, whereas price impact lowers desired positions and adjustment speeds.

Hedge ratios, factor models and diversified portfolios all rest on an estimate of which firms move together. That estimate is not stable: firms migrate between the groupings the market treats as coherent, and when enough migrate the organizing axes of the cross-section turn. We measure the rate of that turning as the mean squared sine of the principal angles between subdominant eigenspaces of consecutive twelve-month S&P 500 correlation matrices. A typical month rewrites a fifth of the structure and carries four-fifths forward. That rate is priced: it couples to the aggregate variance risk premium at t = 5.40, no level measure correlates above 0.32, and the implied-correlation surface spans at most 6.7 percent of it. Only the persistent component is priced - the premium compensates the pace of revision, not the distance traveled. The mechanism is prepayment: implied variance rises on impact, volatility follows two to three quarters later (simulated-null p < 0.03 at h = 1-9), and the premium converges as it arrives. Three pre-registered boundaries hold: no timing alpha, no crash protection, and a downside version inseparable from intensity. The premium is, in part, rent on exposure held over a map still being redrawn.

We introduce Deep-MKV-TS, a path-dependent McKean-Vlasov framework for financial scenario generation. The stochastic dynamics are chosen by matching selected path and volatility features of generated scenarios to those observed in the data. Starting from an interpretable reference model, Deep-MKV-TS preserves the reference drift and adjusts its volatility, while a regularization penalty limits unnecessary departures from the calibrated dynamics. We solve the resulting control problem using a neural, sample-based implementation of the stochastic maximum principle. We validate the method against an exactly computable oracle. On Heston and Heston-mixture models, Deep-MKV-TS substantially reduces path-dependent and volatility-related deficiencies of the reference model. In delayed-volatility experiments, the correction remains effective as the forecasting horizon increases, while direct training becomes less reliable. On held-out intraday equity-index futures, the corrected model improves conditional forecasts relative to the reference and reaches a level of performance comparable to flexible generative and historical baselines. The resulting scenarios also support greater exposure than the reference under a fixed drawdown-risk target. These results show that path-dependent McKean-Vlasov control can enrich an interpretable reference model without replacing it.

Automated market makers (AMMs) are a cornerstone of decentralised finance (DeFi). Constant product markets with concentrated liquidity, such as UniswapV3, are now a well-established design. In these markets, liquidity providers (LPs) face a sequential decision problem: they must decide when to rebalance their positions and which price ranges to allocate capital to as market conditions evolve. We formulate dynamic liquidity provision as a stochastic impulse control problem and use reinforcement learning (RL) to solve it, focusing on providing interpretable solutions. We show that learned policies exhibit rich state-dependent behaviour, allocating liquidity according to mispricing, rebalancing costs, uncertainty, inventory exposure, and heterogeneous risk preferences. These behaviours help compress the left tail of the Profit and Loss (PnL) distribution and avoid catastrophic outcomes under high uncertainty. Finally, we benchmark the RL agents against baseline and sophisticated agents from the AMM microstructure literature and analyse their performance.

We consider the question of the optimal timing of the sale of an asset with stochastic dynamics. Our analysis is based on the method of the distribution builder introduced by Sharpe, Goldstein and Blythe [SGB00] for the purpose of optimal portfolio selection. Instead of specifying a utility function or risk aversion coefficient, this tool directly elicits the target distribution of the investor. We show how the problem of an optimal asset sale is in this setting linked to the problem of finding a Skorokhod embedding of a distribution into a diffusion process. In the case where the asset process follows a geometric Brownian motion and a specific family of distributions is targeted, one can observe a risk-return tradeoff.

The European Union has committed to reducing greenhouse gas emissions 55% below 1990 levels by 2030, but whether current trends are compatible with this ambition remains uncertain. We apply deep learning to high-resolution socioeconomic and sectoral data across EU27 member states till 2023 to project sectoral CO$_2$ trajectories under current trends, extrapolating observed sectoral momentum without assuming changes in the pace or effectiveness of the policy environment beyond what is already reflected in historical data. We project that EU27 emissions will exceed the 2030 target by 35% (620 Mt CO$_2$ shortfall), with only a small minority of countries on trajectories consistent with the bloc's commitments. While the Power sector achieves target-consistent reductions driven by the renewable transition, Mobility shows minimal progress and accounts for over a third of total emissions by 2030, reflecting a structural inertia across member states rather than geographically concentrated lag. Our findings indicate that substantial additional intervention is required to close Europe's ambition-implementation gap, and call for establishing up-to-date energy information in Europe.