Existing financial NLP benchmarks often rely on labels supplied by outside observers, measuring how language is perceived rather than what speakers have committed to in the market. We introduce StakeBench, an evaluation framework for language understanding grounded in market commitment. StakeBench links 560,876 comments from 2,261 resolved markets to verified position, action, and market-odds records across Polymarket and Manifold. Supervision is derived from observable market behavior. Position sides, post-comment trading actions, and market-odds trajectories replace human annotation. Four diagnostic tasks test whether models detect market commitment, identify the revealed side, anticipate future action, and perform collective odds projection. Three commitment-aware metrics measure alignment with revealed preferences rather than perceived sentiment. Validity audits and explicit interpretation boundaries help distinguish observable commitment signals from latent belief and causal market-odds impact. Across 15 LLMs and 18 topics and platform settings, models partially recover position-side signals, with Directed Accuracy from 0.506 to 0.599, but show structural failures on later tasks. Ten of the fifteen models collapse to one or two action labels in future action anticipation, and no model consistently improves on the naive odds-direction baseline in collective odds projection. Model scale is not correlated with performance, finance-domain tuning does not improve revealed-side identification, and platform incentives strongly shape higher-order results. StakeBench is packaged with evaluation code and dataset under CC-BY 4.0.

Predicting stock price movements during Earnings Announcements (EAs) is a significant challenge due to market noise and high-impact price discontinuities. In this study, we evaluate whether pre-announcement news sentiment, firm fundamentals, and recent market dynamics jointly predict the directional price movement of equities on EA days. We construct a multi-modal feature space combining 15 fundamental metrics, 3 price-based technical indicators and sentiment scores derived from financial news articles processed using FinBERT. We compare a Long Short-Term Memory (LSTM) network and a Transformer-based architecture against a logistic regression baseline, and further assess all models with and without sentiment features to quantify their incremental value. Our results indicate that while the LSTM demonstrates higher precision through a conservative safe-bet strategy, the Transformer model exhibits superior sensitivity in identifying volatile movements, achieving a higher macro F1-score, with ablation experiments showing a consistent benefit from incorporating news sentiment.

This paper investigates a mean-field game (MFG) problem for mean-variance (MV) portfolio management, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a piecewise form that depends on whether the individual's wealth is above or below the population average. Due to the inherent time-inconsistency in the MV criterion, together with the piecewise risk aversion, we encounter a class of time-inconsistent MFG, new to the literature. Our goal is to seek a mean-field equilibrium, characterized by a forward-backward stochastic differential equation (FBSDE) system and a mean-field consistency condition. The new challenge stems from the discontinuous coefficients induced by the piecewise risk aversion. In response, we first propose a smooth regularization technique and obtain the existence of the equilibrium in the intra-personal game for the representative agent by establishing the solution to the discontinuous multi-dimensional FBSDE. Next, by invoking fixed-point arguments and convergence analysis as smoothing regularization vanishes, we conclude the existence of the mean-field equilibrium in the time-inconsistent MFG.

The classical tail dependence coefficient (TDC) may fail to capture non-exchangeable features of bivariate tail dependence since it evaluates the underlying copula only along the diagonal. To address this limitation, several measures of strongest manifestation of tail dependence have been proposed in the bivariate case, including a measure based on the tail copula of the underlying bivariate copula. This paper introduces and investigates the multivariate maximal tail concordance measure (MTCM) which extends the bivariate measure to the multivariate case. The MTCM quantifies the largest tail mass over lower hyperrectangles of common unit volume, while the associated maximizer identifies the direction of maximal tail probability. We establish fundamental properties of the MTCM in the multivariate case, including existence of an optimal direction. We also derive analytical representations for several important model classes. Closed-form expressions are further obtained for survival Marshall-Olkin copulas, Archimax and nested Archimedean copulas with regularly varying Archimedean generators. An application to trivariate annual sea-level maxima in England shows that the MTCM can reveal off-diagonal stress directions and substantial differences in the underlying extremal dependence not detected by likelihood- or TDC-based comparisons.

Autonomous AI agents increasingly issue side-effect-bearing actions: database mutations, refunds, payments, external commitments. We propose the Actuarial Action Interface (AAI), a deterministic runtime contract that prices each such action against a contractually fixed safe default under a time-consistent risk mapping, and gates execution against a per-boundary reserve capital budget. We then develop the Authority Frontier, an evaluation primitive measuring how much autonomous authority the runtime releases at each level of reserve capital. The framework provides (i) a deterministic quote-bind-commit protocol with toll-bounded capability tokens; (ii) a universal seven-class action taxonomy mapping heterogeneous tool calls to comparable authority units; (iii) replay determinism and pathwise reserve coverage under alpha-spending; (iv) cross-domain normalization via full reserve demand C_full and capital metrics Capital@k. We instantiate AAI across four agentic environments (database mutation, customer-service refund, and the public tau-bench retail and airline tool-use traces) and report a live Postgres panel in which three Azure-hosted models propose actions through the same contract. The frontier exhibits a common low-reserve refusal and intermediate-release pattern across domains, with saturation only where the budget grid reaches full reserve demand; required reserve capital varies by 22x (Capital@50 from 289 to 6457). The framework does not force domains into the same shape; it surfaces each domain's actuarial geometry. In the live panel the contract prevents realized loss across all three models at low budget while differing in underwriting persistence under denial: model identity is an actuarial underwriting variable. The contribution is a benchmark-ready evaluation framework for runtime actuarial control of autonomous-agent side effects.

Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the first comparison of them by analysing the most prominent example of four-team round-robin competitions, the group stage of the FIFA World Cup. We show that both methods are highly relevant in practice: all (four) deterministic and (six) probabilistic match types occurred in the 2014 and 2018 FIFA World Cups, respectively. The probabilistic model, which accounts for the relative benefits of attacking and defending, provides deeper insights; for instance, the competitive matches from the deterministic approach can be of any of the six probabilistic types. Finally, the probabilistic framework is used to quantify and decompose the impact of the main reforms introduced for the 2026 FIFA World Cup: the expansion to 48 teams, as well as the modified qualification and tie-breaking rules.

Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, Lévy copulas and zero-mixed models, often face practical difficulties in simulation and parameter calibration. In this paper, we introduce the Comb-Bernoulli model, a novel framework for capturing dependence between sparse time series of insurance risks, bridging the benefits of the two standard approaches. The (traditional) copula structure of the proposed model enables tractable: i) simulation, ii) likelihood evaluation, and iii) estimation of dependence parameters. We present the general properties of the model and analyze in detail the Gaussian copula case with lognormal marginals. Moreover, we illustrate an application using the Danish fire insurance dataset, highlighting both the modeling strengths and numerical efficiency of our approach in real-world risk management.

The energy sector is a cornerstone of national strategic autonomy, yet its increasing financialization has transformed ownership structures into complex networked configurations. This paper investigates the distribution of economic power in the Italian energy sector by introducing two sector-level extensions of the Network Power framework: the Aggregate Network Power Index (A-NPI) and the Aggregate Network Power Flow (A-NPF). Unlike traditional macro-level measures, these indices aggregate firm-level control and influence into a systemic framework that accounts for the relative economic weight of each operator. Applying this framework to the Italian case reveals a "Governance Paradox": while the State retains formal majority ownership, the sector's deepening reliance on global capital markets and the pervasive presence of common ownership by transnational institutional investors have progressively hollowed out public strategic direction. The results show that capital centralization enables global financial actors to internalize sectoral competition, fostering a regime of tacit strategic convergence in the management of critical infrastructure. This configuration challenges European strategic autonomy, raising questions about the adequacy of traditional Foreign Direct Investment (FDI) screening and antitrust tools in addressing the systemic influence exerted through networked ownership structures.

Generative artificial intelligence (GenAI) is the first automation wave to reach high-cognitive tasks at scale, yet its effects on intra-urban inequality remain largely unknown. Using 5 million job postings from Beijing (2018--2024), we construct a neighborhood-level GenAI Exposure Index by aggregating task-level assessments from five leading large language models. We examine the spatial, structural and causal mechanisms of this shock. We find that GenAI exposure is highly concentrated in the city's core districts, deepening the intra-urban AI divide. Since 2023, high-exposure neighborhoods have experienced wage stagnation even as they continue to attract high-skilled workers -- a "high-skill trap." This wage penalty is driven by task de-skilling and intensified labor-market crowding. A difference-in-differences design centered on ChatGPT's release supports a causal interpretation. These findings challenge the prevailing theory of skill-biased technological change and provide a basis for inclusive AI governance in global technology hubs.

This paper examines the valuation and hedging of standard equity protection swap (EPS) products proposed by Xu et al.. To account for financial crises and counterparty default risk, we develop pricing frameworks based on Merton's jump-diffusion model and Szimayer's independent random time default model, under which closed-form valuation formulas and put-call parity relations for European options are derived. Hedging strategies for EPS products are analysed under jump and default risks. While static hedging remains effective in the absence of default, counterparty default risk leads to residual losses that cannot be fully hedged. These losses are quantified and used to define default-adjusted initial premiums under both Black-Scholes and jump-diffusion settings. Numerical results illustrate the effects of jump characteristics and default intensity on hedging costs and premiums, highlighting the importance of incorporating crisis and credit risks in EPS pricing and risk management.

We study whether adoption of an AI coding assistant causally expands the technological frontier of individual software developers. We exploit the staggered rollout of Claude Code across GitHub between May 2025 and January 2026 in a panel of 5,838 developers observed monthly over 28 months, with treatment defined by the developer's first Claude-co-authored commit and not-yet-treated developers as controls. Using the doubly robust Callaway and Sant'Anna (2021) estimator, we find positive and significant effects on monthly commits (+41), repositories contributed to (+1.5), distinct programming languages used (+0.83), Shannon language entropy (+0.14), newly-used languages (+0.31), and cumulative lifetime languages (+0.51). The cumulative-languages effect grows with time since adoption, matching a Bayesian-learning model in which AI provides free signals about unfamiliar technologies and lowers the switching barrier. Results are robust to two stricter activity filters. The estimates document a sharp, persistent shift in developer behavior coincident with AI adoption; identification limits prevent a strict causal claim and we outline an agenda for cleaner tests.

Partially convertible economies face a market-design problem: trade integration, cross-border investment, and domestic balance-sheet exposure increase the demand for currency hedging before full financial integration is complete. China adopted a distinctive architecture for this problem by fostering a deliverable offshore Renminbi market (CNH) alongside the segmented onshore market (CNY), rather than relying only on non-deliverable forwards. This creates two venues for closely related claims on the same currency. Spot prices are tightly linked, yet CNY and CNH forwards display a persistent and economically large discrepancy. We study that discrepancy in a joint equilibrium model for spot and forward trading with transaction costs and segmented supply. In the benchmark case with common constant supply and deterministic costs, spot parity implies a forward differential with the wrong sign relative to the data. Random offshore stress, modeled as a jump in trading costs, overturns this benchmark while preserving tight spot parity. The model yields a semi-explicit representation in the CNY/CNH application and a calibration of the observed forward discrepancy in terms of the market-implied likelihood and severity of offshore liquidity stress.

Modelling claim frequency and severity for non-life insurance pricing predominantly relies on generalised linear models, with gradient-boosted machines as the leading machine learning alternative. Tabular foundation models (TFMs) present a fundamentally different inference paradigm. By pre-training on large collections of synthetic datasets, TFMs enable inference on new data through in-context learning, without any dataset-specific fitting or hyperparameter tuning. This paper presents a first empirical evaluation of TabPFN for motor insurance pricing, benchmarking it against GLM and XGBoost on two publicly available MTPL datasets. Our results show that TabPFN does not consistently outperform established baselines, exhibits substantially longer inference times, and is sensitive to the size of the in-context training set. While tabular foundation models represent a promising direction, particularly in data-scarce settings, their current performance does not offer a viable replacement for established actuarial methods.

This paper proposes a public daily-frequency benchmark for post-GFC government-bond CIP deviations. Although CIP deviations are observed daily, the literature lacks a canonical benchmark for daily regressions comparable to standard factor models in asset pricing. Using G10 plus KRW currency-tenor panels, I show that three lagged public state variables-NFCI, the nominal broad U.S. dollar index, and the Treasury 10-year minus 2-year slope-deliver strong in-sample and leave-one-year-out performance. Cointegration, quarter-end, and aggregation-difference diagnostics suggest that the benchmark captures a persistent background component rather than short-maturity quarter-end spikes or spurious level correlation.

Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's dynamics. Recently, score-based diffusion models have learned global diffusion priors that effectively model (stochastic) dynamics, revealing strong potential for data assimilation. In this paper, we investigate how information from noisy observations can be incorporated to enable continuous correction and refinement of the predicted system state when using a diffusion prior. Motivated by particle filtering methods, we represent the posterior distribution using a set of particles. After receiving noisy observations, the diffusion model is guided using the observation likelihood to steer the generation process toward observation-consistent states. Nevertheless, such guidance does not guarantee sampling from the true posterior. We therefore employ a Sequential Monte Carlo approach over the diffusion trajectory, viewed as a path measure, to reweight and resample particles, thereby correcting the generation process and ensuring convergence toward the desired posterior distribution. This leads to an unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.

We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models. Our approach builds on weak-approximation techniques for VIX option prices and yields explicit implied volatility expansions with computable correction terms. The resulting formulas enable fast and accurate calibration without requiring numerical root-finding using option prices. We illustrate the performance of the proposed expansions in both standard and rough Bergomi-type models, as well as in mixed specifications, and demonstrate their accuracy through numerical experiments.

This paper studies the effectiveness and incidence of the renewable energy Investment and Production Tax Credits. I leverage new geographical variation in these credits, introduced by the Inflation Reduction Act, to test whether renewable energy credits had real economic impacts. Communities with greater tax credits accrued 33% more renewable energy capital and produced 31% more renewable energy compared to similar counties. This suggests elasticities of 1.62 and 6.11 for the Investment and Production Tax Credits respectively. I augment these results using an understudied dataset on planned investment to disentangle preplanned from additional projects. Accounting for inframarginal investment significantly reduces the Investment Tax Credit's investment elasticity to 0.6. After characterizing the supply side responses to these renewable tax credits, I document a new political feedback loop between increased incentives and support for renewable energy policies. Areas with greater tax incentives experienced jumps in support for renewable energy policies, contrary to the Not In My Backyard narrative. Heterogeneity in political responses suggests that the Investment and Production Tax Credits garnered support through two channels: 1) labor market spillovers, with construction wages increasing by 7% in areas with greater tax incentives, and 2) public goods spillovers, with parents across party lines increasing support for renewable energy by 13%.

Systemic risk measures play a crucial role in analyzing individual losses conditional on extreme system-wide disasters. In this paper, we provide a unified asymptotic treatment for systemic risk measures. First, we classify them into two families of Value-at-Risk- (VaR-) and expectile-based systemic risk measures. While VaR-based risk measures have been extensively studied, in the latter family, we propose two new systemic risk measures named the Individual Conditional Expectile (ICE) and the Systemic Individual Conditional Expectile (SICE), as alternatives to Marginal Expected Shortfall (MES) and Systemic Expected Shortfall (SES). Second, to characterize general mutually dependent and heavy-tailed risks, we consider a multivariate loss system following a multivariate Sarmanov distribution with common marginal distributions exhibiting second-order regular variation. Third, within this setting, we provide second-order asymptotic results for both families of systemic risk measures. These results extend standard first-order asymptotics and allow for more accurate tail approximations. Through numerical and analytical examples, we demonstrate the superiority of second-order asymptotics in accurately assessing systemic risk. We further conduct a comprehensive comparison between expectile-based and VaR-based systemic risk measures. The results indicate that expectile-based measures often yield higher asymptotic accuracy than VaR-based ones, emphasizing the former's potential advantages in reporting extreme events and tail risk. As a financial application, we use the asymptotic treatment to discuss the diversification benefits associated with various risk measures. Finally, we extend and obtain the second-order asymptotic formulas for generalized-quantile-based systemic risk measures with power functions.

We study a finite-inventory risk-sensitive market making problem in which a dealer controls bid and ask quotes, faces Brownian midprice risk, and receives liquidity-taking orders through point processes with quote-dependent intensities. The objective is the certainty equivalent induced by exponential utility with terminal and running inventory penalties. We introduce an exact discrete entropy-regularized Bellman operator that applies log-sum-exp regularization to deterministic-action certainty-equivalent scores, rather than to a risk-neutral one-step reward. This distinction is essential because the exponential certainty equivalent does not commute with quote randomization. For time step \(h\) and entropy parameter \(λ\), we prove uniform convergence to the unregularized continuous-time risk-sensitive value at rate \[ O\bigl(h+λ(1+|\logλ|)\bigr). \] We also prove certainty-equivalent performance bounds for the induced Gibbs policies under a fresh-sampling relaxed implementation, in which quote marks are sampled at potential fill events rather than frozen over a time step. Under a quadratic growth condition on the Hamiltonian in the relevant quote coordinates, these policies concentrate around the unregularized optimal quote set. Finally, we show that a lower-cost Hamiltonian-Gibbs proxy satisfies a certainty-equivalent performance bound of the same order as the exact Bellman Gibbs policy. Numerical experiments in an Avellaneda--Stoikov specification support the predicted scaling for discretization error, entropy bias, policy gap, quote concentration, and exact-versus-proxy consistency.

Strategic communication often relies on anchors observed by the sender but not by the receiver. An analyst may report against a proprietary valuation model, an auditor against an internal score, a manager against an accounting estimate, or an institution against its own standard. I study a sender-receiver game in which reports are costly to move away from such privately observed anchors. Anchor heterogeneity changes the geometry of communication. Rather than relying on partitions, privately anchored reporting generates continuous variation in messages because different senders find different reports costly to make. This mechanism can improve information transmission, but it can also pull reports toward noisy private anchors. I show that (i) small positive reporting costs can make communication approach full revelation, even though zero costs return the model to cheap talk, (ii) uninformative anchors can transmit information through strategic distortions. Anchored reports and cheap-talk messages can coexist as endogenous hard and soft information, but cheap-talk alone is preferred by all parties under sufficiently low misalignment, explaining why organizations may rely exclusively on informal channels.

This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling. We demonstrate that standard generative models and unconstrained statistical extrapolations suffer from "manifold collapse" and severe arbitrage violations when forecasting term structures across diverse macroeconomic regimes. To overcome this, we propose a two-stage architecture. First, a Student-t Conditional Variational Autoencoder with Dynamic Level Injection (CVAEsT+LS) extracts a robust, heavy-tailed term structure manifold, effectively decoupling macroeconomic shape dynamics from absolute base rates. Second, the latent dynamic evolution is governed by a continuous-time Neural Stochastic Differential Equation (SDE) strictly penalized by a No-Arbitrage Partial Differential Equation (PDE). Empirical results across multiple sovereign currencies (USD, GBP, JPY) confirm that our synergistic approach drastically reduces out-of-sample forecasting errors -- achieving an exceptional 6.58 bps Mean Tenor RMSE -- and successfully overcomes the massive parallel drift and zero-lower-bound violations exhibited by the classical HJM model in extreme environments. Furthermore, through phase space vector field analysis, we demonstrate the model's superior capability in unsupervised macroeconomic regime detection and high-quality continuous-time scenario generation. Ultimately, this research provides a highly scalable, mathematically sound evolutionary engine for term structure modeling.

Put-call parity is a terminal-payoff identity, but its enforcement is capital-using. I study the carry gap, the annualized wedge between option-implied and OIS discount factors, in SPX and RUT index options. Quoted parity is tightly compressed, while the synthetic-traded forward channel leaves a systematic wedge. I interpret this wedge as an implementation premium under finite arbitrage capital. A drift-preserving GBM term, r μ-hat τ, improves in-sample and leave-one-year-out fit, especially in SPX. The evidence suggests that physical drift enters not option payoffs, but the process enforcing risk-neutral parity.

Put-call parity is risk-neutral at terminal payoff, but its enforcement is path-dependent and capital-using. I test whether the SPX and RUT carry gap is explained by OIS-based funding, volatility, trading-friction, and financial-condition variables, or also by residual outside-option information. Adding IEFA, IGOV, and IAU improves in-sample and leave-one-year-out fit after U.S.-centered controls. Gains survive broad-dollar neutralization, alternative blocks, PCA, residualization, and nested horizon selection. Results support reduced-form P-Q alignment: finite-capital parity enforcement reflects physical-measure investment opportunities, not payoff-level no-arbitrage failure.

Put-call parity is a terminal-payoff identity; quoted residuals against traded futures are near zero. Yet enforcing parity is path-dependent, exposing arbitrageurs to daily settlement, margin, and finite capital. Using minute-level NBBO data on S&P 500 and Russell 2000 options, I extract option-implied discount factors, compare them with the OIS curve, and construct an annualized carry gap. A reduced-form specification centered on a volatility times sqrt(tau) path-risk term links the carry gap to implementation risk, trading frictions, and financial conditions, with coefficient signs stable across leave-one-year-out validation. The carry gap is an implementation wedge invisible in price space but systematic in carry space.

Short-horizon option book management relies on P&L expansions in a small set of risk factors. In practice, the quadratic term and common desk adjustments (smile corrections, execution cost add-ons) depend on the chosen factor coordinates, so predicted second-order P&L can change when moving between spot, forward, and log-forward parameterizations. We propose a local, model-agnostic framework that makes the quadratic term coordinate invariant. The usual Hessian is replaced by a covariant Hessian defined by an affine connection, yielding an invariant quadratic predictor. The connection is calibrated to match a desk target for quadratic P&L (Vanna-Volga for smile effects or, in principle, a local fit to realized P&L) while leaving first-order hedge Greeks unchanged. Execution frictions enter through a quadratic cost model for hedge trades. Combined with hedge ratios, this induces an equivalent quadratic penalty on factor moves, makes portfolio netting of costs explicit, and provides local liquidity-aware second-order sensitivities and rebalancing directions. Calibration reduces to small linear systems with clear identifiability conditions. Two FX barrier case studies (EURUSD, USDTRY) illustrate the workflow, and we briefly sketch extensions to other quadratic penalties (risk normalization, scenario/gap terms, and xVA/capital add-ons).

A fast simulation framework for stochastic Volterra processes based on Random Fourier Features (RFF) approximation of the kernel is developed. After recalling the main properties of Volterra processes and reviewing existing numerical simulation methods, an accelerated scheme is introduced that relies on a spectral representation of the kernel. A particular attention is devoted to sampling from the kernel spectral density using Hamiltonian Monte Carlo, whose efficiency and stability bring more convenience than alternative sampling procedures. Quantitative guarantees for the proposed method are established, including moment estimates and strong error bounds. The approach is further compared with the kernel approximation by sum of exponentials commonly used in the literature, emphasizing the broader generality of the present framework. As a primary application, Volterra processes associated with the Stationary fractional Brownian Motion (S-fBM) kernel are investigated. A spectral density representation is derived in closed form using hypergeometric functions, a condition for positive definiteness is established and explicit truncation as well as Monte Carlo error bounds are provided for the RFF approximation in this setting. Numerical experiments in dimensions one and two illustrate the accuracy of the kernel approximation, the reliable recovery of model parameters and the competitiveness of the accelerated simulation scheme in terms of computational efficiency and both weak and strong error performance.

Options are contingent claims regarding the value of underlying assets. The Black-Scholes formula provides a road map for pricing these options in a risk-neutral setting, justified by a delta hedging argument in which countervailing positions of appropriate size are taken in the underlying asset. However, what if an underlying asset is expensive to trade? It might be better to hedge with a different, but related asset that is cheaper to trade. This study considers this question in a setting in which the option written on a portfolio containing $α$ shares of one asset $S_{t_1}$ and $(1-α)$ shares of another security $S_{t_2}$ correlated with $S_{t_1}$. We suppose that the asset is hedged against only one of $S_{t_1}$ or $S_{t_2}.$ In the case of $α=0~\text{or}~1$ we can consider this model to cover the case where an option on one asset is hedged against either the ``right" (underlying) asset or the``wrong" (related, different) asset. We hedge our portfolio on simulated data using varying trading intervals, correlation coefficients, $ρ$ and transaction costs. We calculated the risk-adjusted values ($RAV$) as the risk and return measures to make meaningful decisions on when to trade $S_{t_1}$ or $S_{t_2}.$ From the conclusions made based on $RAV,$ the size of the market price of risk and that of transaction costs on both assets are key to making a decision while hedging. From our results, trading the wrong asset can be opted for when $ρ$ is very high for reasonably small transaction costs for either of the assets.

Given an Itô semimartingale $X$, its Markovian projection is an Itô semimartingale $\widehat{X}$, with Markovian differential characteristics, that matches the one-dimensional marginal laws of $X$. One may even require certain functionals of the two processes to have the same fixed-time marginals, at the cost of enhancing the differential characteristics of $\widehat{X}$ but still in a Markovian sense. In the continuous case, the definitive result on existence of Markovian projections was obtained by Brunick and Shreve~\cite{MR3098443}. In this paper, we extend their result to the fully general setting of Itô semimartingales with jumps.

Large Language Models (LLMs) have recently been leveraged for asset pricing tasks and stock trading applications, enabling AI agents to generate investment decisions from unstructured financial data. However, most evaluations of LLM timing-based investing strategies are conducted on narrow timeframes and limited stock universes, overstating effectiveness due to survivorship and data-snooping biases. We critically assess their generalizability and robustness by proposing FINSABER, a backtesting framework evaluating timing-based strategies across longer periods and a larger universe of symbols. Systematic backtests over two decades and 100+ symbols reveal that previously reported LLM advantages deteriorate significantly under broader cross-section and over a longer-term evaluation. Our market regime analysis further demonstrates that LLM strategies are overly conservative in bull markets, underperforming passive benchmarks, and overly aggressive in bear markets, incurring heavy losses. These findings highlight the need to develop LLM strategies that are able to prioritise trend detection and regime-aware risk controls over mere scaling of framework complexity.

Large Language Models (LLMs) are reshaping knowledge work, yet their impact on voluntary, self-guided open innovation forums (contributors choose tasks without managerial direction) may differ fundamentally from effects observed in organizational settings. We study this question in open-source software development, where individuals' contributions collectively drive innovation at a community level. Unlike product innovation, where typologies for classifying innovation are well established, knowledge work in open-source settings calls for a distinction grounded in the cognitive demand a task places on the contributor. Burgeoning literature distinguishes substantive contributions, which require creative problem formulation to introduce new functionality, from incremental contributions, which draw on comprehension of existing code to maintain and refine it. We exploit a natural experiment around GitHub Copilot's launch in October 2021, where Copilot supported languages like Python while not supporting R for business reasons, creating an exogenous partition between otherwise comparable ecosystems. Using three complementary identification strategies and two classification approaches, we find that Copilot availability increases open-source contributions by 28 to 40 percent. The increase in incremental contributions is significantly larger than the increase in substantive contributions across all specifications. This disparity is more pronounced in projects with higher activity levels and widens following a model upgrade: LLMs function more effectively when existing context helps define the problem and constrain solutions, tilting collaborative innovation toward exploitation of established codebases rather than exploration of new functionality. This paper provides a rare instance of causal field evidence on LLM effects, given the speed at which GenAI has exploded across the knowledge economy.