Papers

We study whether model diversity survives selection into trading. In synthetic markets with a fixed mixture of three language-model families, news presentation changes their representation among submitted orders. At the announcement round, Qwen's share of submitted orders shifts by 48 percentage points in the financing event, with little change in net order counts. In the workforce-reduction event, Mistral's share shifts by 40 percentage points while net counts reverse sign. Homogeneous populations remove opposing flow when their active decisions share a direction. An analytical decomposition shows why selection can improve or worsen price accuracy even at unchanged aggregate demand sensitivity. The evidence concerns presentation bundles and submitted flow; cleaner replication and a known-value validation are specified prospectively.

We consider the distribution-constrained optimal stopping problem $\sup_{\tau\sim \mu} \mathbb E[B^*_\tau]$, where $\mu$ is a probability distribution on $\mathbb R_+$, and $(B^*_t)$ denotes the running maximum of a standard Brownian motion. This problem was introduced in Beiglbock et al. (PTRF, 2018), where a monotonicity principle is used to establish the optimal stopping time as the hitting time of a specific boundary. In this paper, we characterize this boundary by a variational inequality. In the spirit of Cox et al. (PTRF, 2019), we provide a novel probabilistic representation for the variational inequality as a time-reversed optimal stopping problem. A key ingredient for proving the viscosity solution property and comparison principle is a quantitative estimate near the singular corner of the time-space domain, where the initial and boundary conditions are incompatible. We then prove the optimality of the resulting hitting time through a discrete-time Snell envelope construction and a stability argument for the associated stopping times.

The tendency of the double auction mechanism to drive prices to competitive equilibrium has been well documented in laboratory experiments, but the phenomenon has lacked a theoretical explanation. This paper studies dynamic double auctions in a pure exchange economy where agents bid their indifference prices implied by their current holdings and preferences. We show that Walras equilibria coincide with the fixed points of the double auction and that repeated double auctions generate bounded sequences of allocations and prices whose cluster points are Walras equilibria with transfers.

When developers change one component of an agent, such as its controller, a learned model or its verifier, they usually judge the change by an aggregate task score. That score cannot tell whether improvement was attainable, which component lost value, or what the agent's own checks certify. We introduce a claim-specific verification audit for modular agents that plan, act, check and refine. Instead of scoring the agent, the audit scores the evidence: each conclusion is recorded with the evidence behind it, one of four verdicts (supported, unsupported, unresolved or not evaluated) and the boundary within which it holds. Three tools supply that evidence. Oracle policies measure attainable improvement under an explicitly stated action set, so that a low value can be traced to the evaluation rather than to the environment. Replacing one component at a time with a perfect counterpart locates lost value, with null results read as unresolved whenever a downstream component could mask them. A separate test asks whether the verifier's score identifies the quantity it is read as bounding. Applied to a constrained portfolio-allocation agent in a synthetic market with known hidden regimes, the audit shows that the value of perfect regime information depends on the action set used to measure it, that the scenario generator discards most of the regime signal while better local fidelity does not improve decisions, and that the runtime verifier can be bypassed with no visible change in outcomes. The contribution is the protocol and the evidential distinctions it enforces; the empirical findings are specific to the agent and environment studied.

Reinforcement learning for trading often struggles to balance upside participation with drawdown control. Profit-only policies can collapse toward passive long exposure on upward-drifting assets, while aggressively risk-penalized rewards can become too defensive during volatile periods. This paper proposes PPO-HRAP, a hybrid regime-aware policy that combines Proximal Policy Optimization with an interpretable regime prior. The agent observes both market features and portfolio-state variables, receives a reward combining portfolio log return, VIX-conditioned drawdown-increase penalty, target-exposure deviation, and turnover cost, and executes a blended action between the PPO actor output and a regime-derived target exposure. On the held-out 2020-2022 SPY test window, PPO-HRAP achieves 27.62% total return, 8.48% annualized return, 0.6447 Sharpe ratio, 0.8588 Sortino ratio, and 0.4592 Calmar ratio, while reducing maximum drawdown from 34.10% for Buy and Hold to 18.47%. Across five SPY seeds, PPO-HRAP remains stable with mean total return $0.2725 \pm 0.0109$ and mean Sharpe ratio $0.6219 \pm 0.0565$. Single-run cross-asset tests on QQQ and DIA further show that the proposed method ranks first on total return and Sharpe ratio for all three reported assets. These results suggest that blending learned actions with a volatility-aware regime prior is a practical way to improve risk-adjusted trading behavior, although the current policy still incurs high turnover and cross-asset robustness beyond SPY remains limited to single-run evidence.

In global metropolitan areas, public transport benefits from bus systems. Bus design widely applies theoretical models, which typically assume static ridership. However, ridership randomness exists, and lack of attention to it might lead to wrong design decisions. Moving beyond static ridership, we extend the traditional single-line model with stochastic ridership. Further, to optimize the bus system under various ridership randomness, we introduce a hybrid model that combines conventional buses (CBs) and flexible buses (FBs). In both models, we apply a continuous approximation approach and find that: 1) Bus capacity increases with ridership randomness in the extended single-line model; 2) The hybrid model exhibits a binary state: either CBs serve the ridership with rejections under low ridership randomness, or CBs serve the majority while FBs serve the minority with rejections under high ridership randomness. Our findings establish a link between bus system design and ridership randomness, contributing to a more adaptive and efficient public transport framework.

In this work, we study the pricing of American options under stochastic local volatility (SLV) models extended by including stochastic correlation driven by an additional stochastic process. We generalize the class of SLV models by incorporating a flexible stochastic correlation structure. To price options within these extended models, we derive the corresponding reflected forward-backward stochastic differential equations (RBSDEs) and employ data-driven numerical methods to solve them for both pricing and hedging purposes. The RBSDE framework enables the modelling of the future evolution of the option price. Furthermore, we conduct a convergence analysis of the proposed numerical method and present numerical experiments that illustrate the performance of the extended models, as well as the accuracy and efficiency of the RBSDE-based approach.

Statistical validation takes time, and alpha can decay before the evidence justifies deployment. We quantify the surviving opportunity through Certified Alpha Capacity: the maximum expected value remaining under prescribed false-deployment and power constraints. In a canonical Gaussian experiment, we derive an exact certification frontier and the sharp law $\mathcal K_{\alpha,\beta}/\log(1/\varepsilon)$ for residual information capacity just above it. Near the frontier, a single interim decision can preserve orders of magnitude more capacity than fixed-time testing. Mapping information into cash reveals why equally certifiable signals can retain different economic values. In the specified competitive equilibrium, lifetime information approaches the certification frontier exponentially as research costs vanish.

Machine learning predicts outcomes well, but predictive accuracy does not ensure reliable counterfactual responses. We examine how to combine machine learning and theory for measurement and counterfactual analysis, using maritime CO2 emissions where physics provides a benchmark speed response. Matching hourly tracking data for dry bulk and container ships to annual fuel consumption reported under EU regulations, we compare engineering calculations, structural regressions, hybrid models, and machine learning. Out of sample, all estimated models predict within a few percent of reported totals, outperforming standard engineering calculations. Yet pure machine learning and unrestricted structural regression imply attenuated speed responses. Hybrids preserve the structural component's speed response by excluding speed-related inputs from the machine learning component. A cost-benefit analysis of speed reductions illustrates the policy stakes: an attenuated speed response can flip the sign of net benefits. Accurate aggregate predictions therefore cannot substitute for scrutiny of the restrictions determining counterfactual responses.

We study finite-horizon portfolio optimization with proportional transaction costs and trading opportunities arriving at the jump times of a Cox process. Borrowing and short-selling are prohibited, while utility functions need not be concave, increasing, or differentiable. The admissible class includes differentiable utilities with asymptotic elasticity greater than or equal to one. The associated Hamilton–Jacobi–Bellman equation is semi-linear and nonlocal, with control entering only through a zeroth-order term. We show that the normalized equation admits a unique bounded solution that is continuous in all state variables and classical in time and log-price. The proof combines a contraction argument with interior Schauder estimates, and verification identifies the value function and yields an optimal Markovian feedback strategy. Numerical examples with non-concave utilities exhibit, at fixed time and pre-trade wealth, multiple intervals associated with the same trading action, departures from the usual buy–no-trade–sell ordering, and abrupt switches in the optimal post-trade risky weight.

On April 20, 2020, the May front-month WTI oil futures contract, one day before its expiration date, opened near $\$17/$barrel and dropped far below zero in a single trading day, reaching an intraday low of $-\$40.32$ and settling at $-\$37.63$. Such market behavior was unforeseen at the time. This event, and the March 2022 nickel squeeze, illustrate how constraints on physical delivery create pressure to close futures positions and distort futures prices. We develop a feedback model that connects the resulting price distortion to a roll option, and to the imbalance between delivery-constrained long and short positions. Under lognormal benchmark dynamics, the roll-option value is shown to satisfy a pricing PDE which is nonlinear because its payoff depends on the observed futures price, which itself includes the feedback correction. Remarkably, in both cases, there is an explicit solution in terms of classical Black-Scholes-Margrabe exchange option formulas, up to solving a scalar equation. We show this allows that prices may go negative under distortion of a positive-price lognormal model. An analogous construction applies when the lognormal base is switched to Bachelier normal dynamics. Illustrations based on WTI and nickel show the imbalance required to reproduce the extreme event prices under the benchmark assumptions.

Catastrophe bonds have become a central instrument for transferring catastrophic risk to capital markets, yet their payout structures are typically specified exogenously rather than optimized. In this paper, we treat the indemnity function as the decision variable and study the optimal design of CAT bonds from the sponsor's perspective. We establish the optimality of a piecewise linear indemnity function under both expected-disutility and spectral-risk-measure frameworks and thereby reduce an infinite-dimensional design problem to a one-dimensional optimization over the attachment point. The optimal design also eliminates the potential moral hazard associated with the discontinuity of threshold payout structures. We characterize the optimal attachment point under six risk criteria and obtain explicit or semi-explicit solutions. We further derive bounds for the optimal attachment point and develop comparative statics that provide practical design insights. Using U.S. severe storm losses from NOAA's Billion-Dollar Weather and Climate Disasters database for calibration, we show that the optimal CAT bond designs achieve substantial risk reductions across most risk criteria.

This paper examines the post-2010 expansion of the Hungarian construction sector as a case study of large-scale government intervention in a single market. A political economy framework conceptualises the intervention as two mutually reinforcing policies - expansionary demand (public procurement and housing subsidies) and preferential allocation towards politically connected firms - operating under inelastic supply through two mechanisms: market-level subsidy capitalisation and firm-level rent extraction. Using a structured descriptive case study design, the paper draws on Hungarian Central Statistical Office and Eurostat macroeconomic statistics, firm-level data on Hungary's largest companies (CrefoPort), policy documents, and a regional comparison to assess four propositions derived from the framework. The evidence supports all four: real construction output grew faster than in any regional peer except Romania; construction producer prices persistently outpaced the GDP deflator; ownership of the leading firms shifted towards politically connected domestic owners, whose profitability rose sharply while their exports remained negligible; labour productivity per hour worked returned by 2024 to roughly its 2000 level; and connected firms captured a rising share of sector profits, as the subsidies' value was partly eroded by the price increases they induced. Competing explanations do not jointly account for this configuration. The findings illustrate how combined demand stimulus and favouritism produce extensive growth without efficiency gains.

Artificial-intelligence weather prediction (AIWP) models have made it possible to produce high-quality tailored forecasts with limited computational resources. This advance has the potential to benefit hundreds of millions of farmers in low- and middle-income countries who lack access to forecasts of critical weather phenomena. However, it can be difficult for key stakeholders to evaluate forecast quality, risking a "race to the bottom" as cheap but low-quality forecasts crowd out forecasts that would benefit farmers. We propose a set of principles and protocols for evaluating agriculturally-relevant forecasts as a starting point for standards that would let forecasters credibly convey their forecasts' quality.

In this paper, we extend earlier findings of supra-competitive outcomes in optimal-execution games by identifying a learned punitive mechanism that deters deviations and provides behavioural evidence of collusion. We investigate this mechanism in a two-player, finite-horizon Almgren-Chriss liquidation game. Independent proximal policy optimisation agents with access to within-episode price and action histories achieve costs below the Nash benchmark. We identify a profitable deviation by training against the mean learned liquidation schedule, then impose its first trade on one of the original agents. The opponent responds by accelerating liquidation. This response more than offsets the deviator's gain in every run and both player roles, while leaving the punisher's average payoff materially unchanged relative to not punishing under the same deviation. The punisher imposes greater losses on the deviator while preserving its own average payoff, despite the availability of more profitable, less punitive liquidation plans. Matching deviations and subsequent additional selling rise and later decline during training, while final policies retain an effective punitive response. We formalise two checks: whether punishment outweighs the gain from deviating, and whether the change in trading behaviour is large enough to account for the loss imposed. Both checks hold for the tested deviation. Together, these findings provide behavioural and economic evidence supporting a collusive interpretation of the learned supra-competitive outcomes.

Veterans face multiple hardships after they leave the military. Is food insecurity one of these hardships? This paper examines the long-term effects of military service on food insecurity using new data from the PSID. Military veteran-headed households experienced lower food insecurity than non-veteran-headed households, and participated less in federal nutrition assistance programs. We use the Vietnam-era lottery draft to identify causal effects, and find no evidence that military service adversely affects food insecurity. Our results suggest policies that assist currently enlisted service members, and veterans unlikely to head a traditional household, may most effectively tackle food insecurity among military veterans.

We develop a spouse-protected tontine in which a first death changes the household state but generates no pool transfer. The same account remains attached to the household contract until extinction and funds a spouse-only continuation phase if the retiree dies first. We derive contract-level actuarial-fairness conditions and a finite-pool mortality-credit allocation rule with exact ex post budget balance. Under a homogeneous large-pool approximation, we formulate a multidimensional decumulation problem for a representative household, with withdrawal and rebalancing controls while the retiree is alive. The objective balances expected cumulative real household payments against the Conditional Value-at-Risk (CVaR) of terminal shortfalls relative to household reserve targets, without conditioning on survival to the horizon. We develop a numerical solution method for this problem based on a global-in-time neural-network parameterization of admissible control policies. We quantify policy-induced spouse-continuation costs using expected-cost and risk-loaded payment-scale loads at both representative-contract and book levels. We characterize the large-book limit of average per-contract continuation cost as the expected representative-contract cost conditional on common market information. Numerical experiments calibrated to Australia show that the spouse-only phase is a first-order and persistent household event. In these experiments, book-level diversification removes most of the representative-contract excess upper-tail cost of spouse continuation in the large-book limit, without changing expected per-contract continuation cost. A cross-country mortality comparison indicates that the prevalence and persistence of the spouse-only phase are not specific to Australia.

Large language models are strong general-purpose code generators, but executable algorithmic trading remains a demanding specialization target: a model must translate a natural-language strategy specification into correct program logic for a specialized trading framework, execute on historical data, produce trades, and remain semantically faithful to the request. We study two complementary mechanisms for specializing language models for this setting: continued pretraining on algorithmic-trading framework code and supervised fine-tuning (SFT) on agent-validated request-to-code pairs. Evaluation is centered on QuantCode-Bench, our 400-task benchmark for Backtrader strategy generation, together with a repository-level SWE-bench-like track. Continued pretraining improves single-turn Judge Pass from 41.5% to 47.5% for Qwen3.5-397B-A17B and from 27.8% to 33.0% for Qwen3.6-35B-A3B. SFT applied after continued pretraining yields a larger gain for Qwen3.6-35B-A3B, reaching 58.2% Judge Pass and 83.5% successful backtests; in agentic evaluation it raises first-turn success from 22.3% to 58.3% and final success after up to 10 turns from 47.5% to 79.5%. Continued pretraining alone improves first-turn agentic success but lowers final success after repair from 47.5% to 32.5%, consistent with degraded instruction following, whereas SFT improves both. We also identify a capability-retention failure: domain specialization degrades parser-conformant structured tool calling, and targeted recovery SFT restores tool-call formatting but not the base checkpoint's repository-level agent performance. The results show that framework-oriented pretraining, validated SFT, and explicit capability-retention evaluation address distinct failure modes in domain-specific executable code generation.

Many of the thousands of existing cryptocurrencies suffer from declining adoption, low liquidity and weak security, and merging two of them into a single ecosystem is a natural alternative to abandonment. No rigorous framework exists, however, for determining a fair exchange rate in such a merger. Unlike that of a corporation, the value of a cryptocurrency is driven by network effects, so the exchange rate itself influences the value of the merged asset. We extend the exchange-ratio framework of Mainini, Moretto and Visetti [7] by making the merged value endogenous: the exchange rate determines community migration, migration determines (up to user overlap) the post-merger network state, and an axiomatised valuation function assigns a value to that state. The resulting synergy has no predetermined sign, and the bounds of the bargaining region become self-referential in the exchange rate. We prove that no exchange rate at which the merger destroys value preserves wealth, and that the pre-merger price ratio preserves wealth exactly when the merger does not destroy value at that rate. In that case, under explicit threshold conditions, the price ratio satisfies all five of our fairness conditions – wealth, adoption, security, governance and liquidity preservation – and, under strict versions of these conditions, the admissible set contains a nondegenerate interval around it, the wealth-admissible set one of explicit width. The network-value laws proposed in the literature, from the linear law to Metcalfe's and its generalised power-law forms, share a convexity property that yields the Lipschitz control behind these estimates. Liquidity emerges as the only non-wealth condition that can disconnect the admissible set.

Decision-focused learning (DFL) trains predictors through downstream objectives, but a different loss need not provide an independent parameter-update direction. We characterize this restriction through the predictor Jacobian, using sparse index tracking to distinguish the covariance entries read by the optimizer from the parameter directions available to learning. Rank-one Jacobians make nonzero per-example gradients collinear; a conditional spectral bound describes near-collinearity. A batch-subspace characterization and counterexamples show why these local statements imply neither common minimizers nor collinear batch updates. Experiments examine when geometry translates into decision quality. Across 38 one-parameter equity configurations, DFL gains over MSE remain below 1.8%; a 385-parameter conditional predictor also has pointwise rank one. In validation-tuned shortest-path and knapsack experiments, full-capacity SPO+ reduces mean regret by 11.6% and 10.6%, respectively; only knapsack survives correction across eight comparisons. The capacity contrast persists on fresh datasets across batch orders and training budgets. Holding expressivity fixed, invertible coordinate scaling lowers spectral effective rank and ordinary SGD gains; compensating for the scaling restores the original trajectories. Financial forward-target controls separate forecast accuracy from decision quality; a matched neural comparison finds no aggregate DFL advantage in the tested architecture. These findings distinguish local rank restrictions, coordinate-dependent optimization and predictive accuracy. Predictor geometry helps explain available learning directions, while held-out decision quality remains the test of practical benefit.

European option smiles determine the risk-neutral marginal laws of an asset, but not their intertemporal coupling, which is decisive for many applications. The Bass martingale construction selects, among all calibrated martingales, the one closest to Bachelier dynamics; it permits fast calibration at discrete maturities and recovers the Dupire local-volatility (LV) model as the maturity grid is refined. This article develops a modular calibration overlay for existing stochastic and path-dependent volatility models. We sequentially construct a martingale that matches all prescribed marginals exactly while remaining as close as possible, in an adapted Knothe-Rosenblatt sense, to the reference dynamics. As with the Bass LV model, each calibration step is amenable to an efficient Martingale Sinkhorn algorithm. We develop the theoretical foundations, numerical implementation and consider convergence to the SLV model. We also benchmark the method for Heston and Bergomi finite-factor path-dependent volatility dynamics and develop the multi-asset extension.

Bank treasury portfolios must balance yield, liquidity, and interest-rate risk across bonds of different maturities. Static allocation rules are ill-suited to this task: portfolios concentrated in long-duration securities with no dynamic adjust- ment mechanism can accumulate large mark-to-market losses and liquidity stress under rising interest rates, as illustrated by the failure of Silicon Valley Bank in 2023. We develop a tractable simulation-based framework for multi-period bond port- folio optimization under interest-rate risk and proportional transaction costs. Yield-curve dynamics are modeled using the Dynamic Nelson-Siegel parameter- ization with Vector Autoregressive factor dynamics, from which we construct a time-inhomogeneous discrete-state Markov chain approximating the joint yield process across bond maturities. This chain forms the state space of a finite- horizon Markov Decision Process in which the investor maximizes expected terminal wealth subject to proportional rebalancing costs. The optimal portfolio policy is obtained by backward induction. We also quantify the approximation error introduced by truncating the transition kernel, and show that it leaves mean terminal wealth almost unchanged while substantially distorting drawdown and tail statistics.

We derive a short-maturity expansion for up-and-out put barrier option prices under continuous stochastic volatility when the strike and the barrier approach the spot at the diffusive scale. Assuming joint weak convergence of the normalized terminal return, the relative volatility fluctuation, and the running maximum, together with uniform integrability, we show that the leading term is the time-inhomogeneous Black-Scholes barrier price fitted to the forward variance curve. The first model-dependent correction is of order $\theta^{H+1/2}$, where $\theta^H$, $H \in (0,1/2]$, is the order of the relative volatility fluctuation, and is represented explicitly through killed Brownian transition densities. For regular volatility models, where $H= 1/2$, the coefficient is determined by the short-maturity at-the-money implied-volatility skew. For rough volatility models with $H < 1/2$, the coefficient reduces to a one-dimensional integral. Numerical experiments show that the correction materially improves the Black-Scholes approximation.

Machine-learning signals built from financial text treat what institutions say, and what the media repeat, as evidence about value. But whoever shapes a narrative may be trading against it. We study markets with three observable voices: institutional statements (Say), media repetition (Echo) and revealed positioning (Do). We ask when words should be followed and when they should be faded. In a linear-quadratic model of an informed institution that speaks and trades before a partly credulous crowd, talking an asset down while buying it is optimal exactly when $\varphi^2<2\lambda k<\varphi$. A distribution-free identity then shows that when the observable Say-Do covariance is negative, words carry negative predictive content and should be faded. For measurement, we derive (i) an exact factorised posterior over which articles are echoes, combining arrival times with embedding similarity; (ii) a return-aligned contrastive objective that attains its bound exactly when squared embedding distances are an increasing affine function of squared outcome distances, with the tightest loss-based certificate of which neighbour rankings survive imperfect training; and (iii) a path-signature statistic for who moved first. In a controlled market with known ground truth, echo sentiment predicts returns with a significantly negative sign in all 29 simulated markets, the rolling Say-Do correlation flags false-alarm events with an AUC of 0.90, and return-aligned embeddings organise headlines by consequence rather than topic. We also report where the tools fail.

Human verification depends on expertise that must be maintained before it is needed. This paper links reliance on automated checks, investment in human checking ability, and performance during an interruption. Better checking lowers the error reduction gained from an extra unit of human skill while the checker works. It can therefore reduce the incentive to preserve independent expertise, even when it lowers the best achievable expected cost of maintenance and errors. In an illustration, a more informative checker raises detection while it works from \hoPowWorkA{} to \hoPowWorkC{} percent, but the organization then keeps no routine practice and detects \hoPowOnsetC{} percent of errors when the checker first fails, against \hoPowOnsetA{} percent with a less informative checker. A detection requirement therefore concerns both current capability and its survival until new training becomes effective. Evidence from colonoscopy and aviation documents weaker unaided performance under routine automation, without isolating the mechanism. The framework connects a detection target to an explicit reserve of expertise and a training pipeline. Standard detection tests estimate each quantity and reveal automation bias and silent checker failures. The framework distinguishes the requirement from minimizing expected loss and proposes a longitudinal test.

Liquidity provision in automated market makers is typically analyzed at the pool level, implicitly assuming LP homogeneity. This aggregate view can hide how liquidity provision outcomes differ between LP strategies, particularly as concentrated liquidity AMM designs operating on high-performance blockchains allow liquidity to be actively repositioned around trades. We develop a markout-based framework to decompose Uniswap LP profitability into active and passive components using two complementary methods: a LIFO subtraction method that matches short-lived mint-burn positions and attributes swap-level markouts by liquidity share; and an infinitesimal LP benchmark that estimates the performance of a fully passive, always-in-range marginal LP directly from the AMM price path. We apply these methods to Uniswap v2, v3, and v4 pools on Ethereum, Arbitrum, and Base chains, and find passive profitability can materially differ from aggregate pool profitability. In Uniswap v2, with liquidity distributed evenly and active LP behavior nearly absent, the overall and passive markouts are almost the same. In contrast, concentrated-liquidity pools have a systematic active-passive gap: passive LPs tend to underperform aggregate pool-level measures. The gap is wider on Ethereum than on L2s, consistent with active liquidity provision being more useful when block times and ordering conditions allow LPs to react to incoming flow. In general, passive LPs perform better on higher fee pools. The LIFO and infinitesimal estimates are generally consistent directionally across most pools, providing evidence of the robustness of the decomposition. The results suggest that adverse selection in AMMs is not evenly distributed among LPs, with important implications for LP strategy, fee-tier design and measurement of DEX market quality.

Network reconstruction from partial information is usually performed at the same resolution level at which constraints are observable. This becomes problematic when only coarse-grained information is available, while the relevant process occurs at a finer scale. Here we employ the multiscale model of weighted networks introduced in a companion paper and turn it into a probabilistic framework for reconstructing weighted networks across arbitrary aggregation levels. The model is built to preserve its functional form under coarse-graining, so that global parameters calibrated on an observable aggregate layer can be transferred to finer layers without refitting. We test the method on two empirical systems with different aggregation mechanisms. In the International Trade Network, countries are aggregated into geographic macro-regions and the observed coarse-grained layer is used to infer the underlying country-level network. In the Dutch production network, sectoral flows are reconstructed across the hierarchical industrial classification, using coarser sectoral layers to infer finer ones. In both geographical and sectoral settings, we benchmark our genuinely multiscale reconstruction method against a state-of-the-art weighted reconstruction model calibrated directly at the target resolution, and therefore using additional information available at the same (finer) scale at which performance is evaluated. Remarkably, despite this informational disadvantage, our method recovers the fine-scale binary structure with high accuracy, improving precision, specificity, accuracy and maximum degree-error diagnostics, while remaining nearly equivalent in sensitivity.

Power systems with increasing variable renewable generation face greater uncertainty in scheduling and balancing. Intraday and balancing electricity markets facilitate position adjustments and real-time balancing close to delivery. As delivery approaches, continuous intraday market participants exposed to imbalance settlement adjust their positions by trading additional volumes to reduce their imbalance exposure. We conjecture that positions remaining open after intraday trading, together with demand and supply uncertainties affecting physical market participants, influence price formation in the balancing market. This cross-market interaction is, however, rarely studied. To understand this interaction, this paper uses probabilistic modeling to examine how intraday orderbook information reflects subsequent imbalance price formation in Germany and Austria. We compare orderbook representations based on open, high, low, close, and volume, Volume-Weighted Average Price (VWAP), and last mid price across multiple horizons. Each representation is evaluated using the self product, neighboring products, and the product from the neighboring country. We then compare the best orderbook setting with fundamental feature sets and their combinations, followed by an ablation study of the available training history. We show that VWAP with neighboring products provides the best performance in both countries. Combining orderbook and fundamental information reduces testing loss in Germany but increases it in Austria. Using all available observations provides the best overall performance, while excluding 2022 can reduce loss for extreme price samples. These results reveal and help explain country-dependent interactions between the intraday and balancing markets.

This work studies the relationships among sublinear valuation rules, uncertainty structures, and local specifications in a time-homogeneous Markovian framework with killing. These objects are linked, under finiteness and locality of the upper generator and a Lyapunov condition, by three maps: robust valuation, globalization, and localization. First, we show that the corresponding classes of uncertainty structures and sublinear valuation rules are order-isomorphic via the robust valuation map. Second, our analysis clarifies how local specifications constrain sublinear valuation and uncertainty structures, as well as what information localization and globalization preserve. In particular, the compositions of localization and globalization need not recover the original objects but yield canonical extremal elements. Third, the sublinear valuation generated by a local specification is characterized by the greatest viscosity subsolution of the associated Hamilton–Jacobi–Bellman equation. Finally, each uncertainty structure with killing admits a unique representation by a family of pairs consisting of a cumulative discounting process and an underlying state law. These results provide a framework for order relations, probabilistic and PDE-based representations, and model recovery in sublinear valuation without requiring uniqueness of the underlying martingale problems or a viscosity comparison principle.

We model market impact as the response to submitted order flow net of counterflow from latent traders, activated when price displacements from the level that would prevail without the order exceed individual thresholds. Order flow depletes this pool, and a generalized Langevin equation governs its recovery over several time scales. Its memory kernels are finite sums of exponentials, so its Markovian lift is exact rather than an approximation. For an undepleted pool, aggregation under explicit assumptions on individual trading responses yields an intermediate square-root regime between linear small- and large-order limits, without imposing a square-root impact law. Scaling thresholds and responses with price noise makes impact in this regime proportional to volatility, and thresholds that grow with the execution horizon make it independent of duration. With constant displayed depth, expected round-trip costs are nonnegative under the log-price convention, independently of the memory. Numerical experiments show that depletion narrows the square-root range and that memory spectra producing similar single-order impacts can respond differently after substantial prior trading. Calibration to market data is left to a companion paper.