This paper studies the problem of hedging and pricing a European call option under proportional transaction costs, from two complementary perspectives. We first derive the optimal hedging strategy under CARA utility, following the stochastic control framework of Davis et al. (1993), characterising the no-transaction band via the Hamilton-Jacobi-Bellman Quasi-Variational Inequality (HJBQVI) and the Whalley-Wilmott asymptotic approximation. We then adopt a deep hedging approach, proposing two architectures that build on the No-Transaction Band Network of Imaki et al. (2023): NTBN-Delta, which makes delta-centring explicit, and WW-NTBN, which incorporates the Whalley-Wilmott formula as a structural prior on the bandwidth and replaces the hard clamp with a differentiable soft clamp. Numerical experiments show that WW-NTBN converges faster, matches the stochastic control no-transaction bands more closely, and generalises well across transaction cost regimes. We further apply both frameworks to the bull call spread, documenting the breakdown of price linearity under transaction costs.

We derive the stochastic price process for tokens whose sole price discovery mechanism is a constant-product automated market maker (AMM). When the net flow into the pool follows a diffusion, the token price follows a constant elasticity of variance (CEV) process, nesting Black-Scholes as the limiting case of infinite liquidity. We obtain closed-form European option prices and introduce liquidity-adjusted Greeks. The CEV structure generates a leverage effect -- volatility rises as price falls -- whose normalized implied volatility skew depends only on the pool's weighting parameter, not on pool depth: Black-Scholes underprices 20%-out-of-the-money puts by roughly 6% in implied volatility terms at every pool depth, while the absolute pricing discrepancy vanishes as pools deepen. Empirically, after controlling for pool depth and flow volatility, realized return variance across 90 Bittensor subnets exhibits a strongly negative price elasticity, decisively rejecting geometric Brownian motion and consistent with the CEV prediction. A complementary delta-hedged backtest across 82 subnets confirms near-identical hedging errors at the money, consistent with the prediction that pricing differences are concentrated in the wings.

I derive a size premium from the constant-product automated market maker used to price Bittensor subnet tokens and test the prediction using daily data on 128 subnets. A small-minus-big factor earns 1.01% daily (Newey-West t = 3.28). The December 2025 halving of token emissions, which the theory predicts should halve the premium, reduces it from 1.17% to 0.51% (p = 0.044). Exact slippage calculations show the premium is implementable only below \$10K in assets under management; at \$100K, transaction costs exceed gross returns.

The proliferation of diverse, high-leverage trading instruments in modern financial markets presents a complex, "noisy" environment, leading to a critical question: which trading strategies are evolutionarily viable? To investigate this, we construct a large-scale agent-based model, "MAS-Utopia," comprising 10,000 agents with five distinct archetypes. This society is immersed in five years of high-frequency data under a counterfactual baseline: zero transaction friction and a robust Unconditional Basic Income (UBI) safety net. The simulation reveals a powerful evolutionary convergence. Strategies that attempt to fight the market's current - namely Mean-Reversion ("buy-the-dip") - prove structurally fragile. In contrast, the Trend-Following archetype, which adapts to the market's flow, emerges as the dominant phenotype. Translating this finding, we architect an LLM-driven system that emulates this successful logic. Our findings offer profound implications, echoing the ancient wisdom of "Be Water": for investors, it demonstrates that survival is achieved not by rigid opposition, but by disciplined alignment with the prevailing current; for markets, it critiques tools that encourage contrarian gambling; for society, it underscores the stabilizing power of economic safety nets.

Classical correlation and rolling PCA summarize market dependence through covariance spectra, but they do not provide a unified operator representation for entropy, purity-based mixing, and standardized structural deviations built from rolling multi-feature trajectories. We propose the Quantum Network of Assets (QNA), a quantum-inspired but non-physical density-operator framework in which normalized asset-level state vectors induce a time-varying market operator and an associated overlap network. The framework yields two structural diagnostics: the Entanglement Risk Index (ERI) and the Quantum Early-Warning Signal (QEWS). Using a stable NASDAQ-100 panel over 2020-2025, spanning the pandemic aftermath, the 2022 tightening cycle, and the 2025 tariff repricing episode, we show that QNA entropy remains strongly related to covariance spectral entropy and effective rank at the regime level, but that the method becomes empirically distinct once the operator is constructed from multi-feature rolling trajectories rather than returns alone. In the returns-only limit, QNA lies close to classical spectral summaries; with volatility and liquidity channels included, it captures broader dependence reconfiguration and produces the clearest incremental signal during the April 2025 tariff escalation, when QEWS shifts sharply while rolling-z classical spectral benchmarks move only modestly. QNA therefore does not replace covariance-spectrum methods; instead, it provides a unified operator representation in which entropy, purity-based mixing, and event-aligned structural deviations are analyzed jointly across rolling multi-feature market states.

We give an overview on the emerging applications of GenAI in the financial industry, especially within investment banks. Inherent to these exciting opportunities is a new realm of risks that must be managed properly. By heeding both the Yin and Yang sides of GenAI, we can accelerate its organic growth while safeguarding the entire financial industry during this nascent era of AI.

This paper studies proportional risk sharing at claim occurrence time in community-based insurance. Each participant is modeled by an individual Cramér-Lundberg surplus process, and, whenever a claim is reported within the pool, its cost is redistributed according to a fixed allocation matrix. We compare the infinite-time ruin probability of each participant under stand-alone operation and under pool participation. Our main result shows that pooling reduces, for every participant, the infinite-time ruin probability when claim severities belong to a common scale family, the allocation rule satisfies full allocation and actuarial fairness, and each transfer remains bounded by an individual capacity condition. The proof relies on a convex-order comparison between the losses borne inside the pool and the corresponding stand-alone losses. We also clarify the role of these assumptions by showing that, outside this framework, pooling need not be beneficial for all participants. Numerical illustrations with Exponential and LogNormal severities support the theoretical findings and highlight how the design of proportional sharing rules affects solvency. The paper thus provides simple and interpretable sufficient conditions under which transparent linear risk-sharing arrangements improve individual solvency in community-based insurance.

Options with maturities below one week, hereafter "ultra-short-term" options, have seen a sharp increase in trading activity in recent years. Yet, these instruments are difficult to price jointly using classical pricing models due to the pronounced oscillations observed in the at-the-money implied-volatility term structure across ultra-short-term tenors. We propose Edgeworth++, a parsimonious jump-diffusion model featuring a nonparametric stochastic volatility component, which provides flexibility in capturing implied-volatility smiles for each tenor, combined with a deterministic shift extension, which allows the model to fit rich at-the-money implied-volatility shapes across tenors. We derive a local (in tenor) expansion of the process characteristic function suited to value ultra-short-term options. The expansion leads to fast and accurate option pricing in closed form via standard Fourier inversion. We discuss the benefits of the proposed approach relative to benchmarks.

Time-of-use pricing is promoted to manage demand at public EV charging stations, yet its effectiveness depends on short run flexibility and local constraints. Using station by day by hour data from Shenzhen and Amsterdam, we estimate intraday price responsiveness on two margins, whether charging occurs in a station hour and, conditional on charging, delivered energy and occupancy time. High dimensional fixed effects absorb station by day demand shocks and hour of week patterns, so identification relies on within station, within day price variation under scheduled tariffs. Responses differ across cities. Shenzhen adjusts mainly through conditional intensity, whereas Amsterdam adjusts mainly through participation. Weather shifts responsiveness in opposite directions, with heat weakening responses in Shenzhen and rainfall strengthening participation responses in Amsterdam. Power upgrades typically outperform network densification except in transit-oriented areas.

The standard wage Phillips curve aggregates away from which workers reset wages when. I show this aggregation omits a first-order term: the covariance between workers' cost-push exposure and their reset frequency. I introduce two sufficient statistics and embed them in a multi-country HANK model calibrated to six euro-area economies. The omitted term generates 7 percent more cumulative core inflation in the baseline and 10--26 percent more when monetary policy is delayed. Two economies with identical openness can differ by 6.6 percentage-point-quarters solely from within-country composition. Targeted essentials subsidies reduce welfare loss by 32 percent relative to aggressive tightening. Out of sample, the model correctly predicts the persistence ranking across the UK, the US, and Japan.

This paper develops a unified framework for evaluating the optimal degree of task automation. Moving beyond binary automate-or-not assessments, we model automation intensity as a continuous choice in which firms minimize costs by selecting an AI accuracy level, from no automation through partial human-AI collaboration to full automation. On the supply side, we estimate an AI production function via scaling-law experiments linking performance to data, compute, and model size. Because AI systems exhibit predictable but diminishing returns to these inputs, the cost of higher accuracy is convex: good performance may be inexpensive, but near-perfect accuracy is disproportionately costly. Full automation is therefore often not cost-minimizing; partial automation, where firms retain human workers for residual tasks, frequently emerges as the equilibrium. On the demand side, we introduce an entropy-based measure of task complexity that maps model accuracy into a labor substitution ratio, quantifying human labor displacement at each accuracy level. We calibrate the framework with O*NET task data, a survey of 3,778 domain experts, and GPT-4o-derived task decompositions, implementing it in computer vision. Task complexity shapes substitution: low-complexity tasks see high substitution, while high-complexity tasks favor limited partial automation. Scale of deployment is a key determinant: AI-as-a-Service and AI agents spread fixed costs across users, sharply expanding economically viable tasks. At the firm level, cost-effective automation captures approximately 11% of computer-vision-exposed labor compensation; under economy-wide deployment, this share rises sharply. Since other AI systems exhibit similar scaling-law economics, our mechanisms extend beyond computer vision, reinforcing that partial automation is often the economically rational long-run outcome, not merely a transitional phase.

Business cycle synchronization between EU and Western Balkan candidate economies is usually modeled with aggregate time-domain correlations that mix short-run and long-run dynamics. This paper addresses that limitation by combining wavelet-based time-frequency decomposition with Bayesian zero-inflated beta regression. Using annual dyad-year data for 2001--2021, we estimate synchronization separately at shorter (1.5--4.5 years) and longer (4.5--8.5 years) horizons and relate each horizon to its correlates. The results show that EU--WB dyads are less synchronized than EU--EU dyads in the short run, and that trade deepening over time is more positively associated with short-run synchronization in EU--WB pairs. At longer horizons, the positive association between shared EU/EMU membership and synchronization weakens or reverses when the same country pair moves into deeper institutional integration, while differences across country pairs in average EU/EMU status become negligible. Over the same horizon, trade deepening within a pair is more consistently associated with synchronization, and more persistent structural dissimilarity is associated with lower synchronization. EU--WB dyads are no longer clearly less synchronized at these frequencies, and the remaining convergence pattern is more consistent with sectoral differences narrowing over time than with trade. These findings indicate that synchronization channels are horizon-dependent and that conclusions based on single-horizon correlation measures can obscure the distinction between short-term coupling and structural convergence.

We study scaled trinomial models converging to the Black--Scholes model, and analyze exponential certainty-equivalent prices for path-dependent European options. As the number of trading dates $n$ tends to infinity and the risk aversion is scaled as $nl$ for a fixed constant $l>0$, we derive a nontrivial scaling limit. Our analysis is purely probabilistic. Using a duality argument for the certainty equivalent, together with martingale and weak-convergence techniques, we show that the limiting problem takes the form of a volatility control problem with a specific penalty. For European options with Markovian payoffs, we analyze the optimal control problem and show that the corresponding delta-hedging strategy is asymptotically optimal for the primal problem.

Surveillance of diseases in a pandemic is an important part of public health policy. Diagnostic testing at the individual level is often infeasible due to resource constraints. To circumvent these constraints, group testing can be applied. The economic cost evaluation from the payer's perspective typically focuses only on deterministic costs which overlooks the substantial economic impact of productivity losses resulting from quarantine and workplace disruptions. The objective of this article is to develop a mathematical model for a retrospective economic evaluation of group testing that incorporates both deterministic costs and income-based economic loss. Group testing algorithms are revisited and simulated at optimized pool sizes to determine the required number of tests. Income data from the German Socio-Economic Panel are integrated into a mathematical model to capture the economic loss. Afterward, hybrid Monte Carlo experiments are conducted by evaluating the economic cost in the Coronavirus disease 2019 pandemic in Germany. Monte Carlo experiments show that the optimal choice of group testing algorithms changes substantially when income-based economic losses are included. Evaluations considering only deterministic costs systematically underestimate the total economic cost. Algorithms with a longer quarantine duration are less attractive than shorter quarantine duration if income-based economic loss is accounted for. The findings show that current evaluations underestimate the true economic cost. Group testing algorithms with shorter duration and fewer stages are preferred, even when they require a larger number of tests. These results underscore the importance of incorporating income-based economic loss into a mathematical model.

We address the problem of executing large client orders in continuous double-auction markets under time and liquidity constraints. We propose a model predictive control (MPC) framework that balances three competing objectives: order completion, market impact, and opportunity cost. Our algorithm is guided by a trading schedule (such as time-weighted average price or volume-weighted average price) but allows for deviations to reduce the expected execution cost, with due regard to risk. Our MPC algorithm executes the order progressively, and at each decision step it solves a fast quadratic program that trades off expected transaction cost against schedule deviation, while incorporating a residual cost term derived from a simple base policy. Approximate schedule adherence is maintained through explicit bounds, while variance constraints on deviation provide direct risk control. The resulting system is modular, data-driven, and suitable for deployment in production trading infrastructure. Using six months of NASDAQ 'level 3' data and simulated orders, we show that our MPC approach reduces schedule shortfall by approximately 40-50% relative to spread-crossing benchmarks and achieves significant reductions in slippage. Moreover, augmenting the base policy with predictive price information further enhances performance, highlighting the framework's flexibility for integration with forecasting components.

This paper introduces a methodology for constructing a market index composed of a liquid risky asset and a liquid risk-free asset that achieves a fixed target volatility. Existing volatility-targeting strategies typically scale portfolio exposure inversely with a variance forecast, but such open-loop approaches suffer from high turnover, leverage spikes, and sensitivity to estimation error -- issues that limit practical adoption in index construction. We propose a proportional-control approach for setting the index weights that explicitly corrects tracking error through feedback. The method requires only a few interpretable parameters, making it transparent and practical for index construction. We demonstrate in simulation that this approach is more effective at consistently achieving the target volatility than the open-loop alternative.

Electricity price forecasts are typically evaluated using accuracy measures such as RMSE and MAE, although these metrics often fail to reflect their economic value in operational decisions. This paper investigates which statistical properties of electricity price forecasts are most relevant for economic performance, using battery energy storage system (BESS) arbitrage as an application. We assess prediction quality along four dimensions: forecast accuracy, intraday error dispersion, association between predicted and realized prices, and the ability to identify daily price extrema. We construct a comprehensive pool of 192 hourly day-ahead electricity price forecasts and use it to evaluate the relationship between proposed quality measures and profits generated for two representative BESS configurations. The results show that traditional accuracy metrics are only weakly correlated with BESS income. At the same time, dispersion- and association-based measures better capture a forecast's economic value by reflecting its ability to reproduce daily price patterns. These findings demonstrate that incorporating complementary evaluation criteria may improve forecast selection and enhance the economic performance of BESS.

We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional case to the 2-dimensional setting and is applicable for general Lévy measures under mild assumptions. A tailored discretization of the non-local integral term is developed, which can be efficiently evaluated by means of the fast Fourier transform. For the temporal discretization, the semi-Lagrangian theta-method is employed in a convenient splitting fashion, where the diffusion term is treated implicitly and the integral term is handled explicitly by a fixed-point iteration. Numerical experiments for put-on-the-average options under Normal Tempered Stable dynamics reveal favourable second-order convergence of our method whenever the exponential Lévy process has finite-variation.

In the context of micro-finance, a group of individuals undertake business projects that may interfere with one another. A contagious default happens if one person's project failure leads to the default of another group member. In this paper, we apply a probabilistic approach to analyze the impact of such contagion among investment group members. Firstly, a general formula is provided to compute the group survival probability with the presence of contagion effect. Then, special cases of this probability model are examined in detail. In particular, we show that if the investment group is homogeneous, defined in the paper, then including more members into the group will eventually lead to default with probability 1. This differs from the non-contagious scenario, where the default probability decreases monotonically with respect to the group size. Afterwards, we provide an upper bound of the optimal group size under the homogeneous setup; so, one can run a linear search within finite time to locate this optimizer.

As variable renewable energy increases and more demand is electrified, we expect price formation in wholesale electricity markets to transition from being dominated by fossil fuel generators to being dominated by the opportunity costs of storage and demand management. In order to analyse this transition, we introduce a new method to investigate price formation based on a mapping from the dual variables of the energy system optimisation problem to the bids and asks of electricity suppliers and consumers. This allows us to build the full supply and demand curves in each hour. We use this method to analyse price formation in a sector-coupled, climate-neutral energy system model for Germany, PyPSA-DE, with high temporal resolution and myopic foresight in 5-year steps from 2020 until full decarbonisation in 2045. We find a clear transition from distinct price levels, corresponding to fossil fuels, to a smoother price curve set by variable renewable energy sources, batteries and electrolysis. Despite higher price volatility, the fully decarbonised system clears with non-zero prices in 75% of all hours. Our results suggest that flexibility and cross-sectoral demand bidding play a vital role in stabilising electricity prices in a climate-neutral future. These findings are highly relevant for guiding investment decisions and informing policy, particularly in support of dynamic pricing, the expansion of energy storage across multiple timescales, and the coordinated development of renewable and flexibility technologies.

While financial misconduct in advisory services persists despite regulation, the demand-side of market discipline, specifically the timing of investor detection, remains a critical bottleneck. Using approximately 55,700 FINRA BrokerCheck records, we analyze the detection lag between misconduct inception and formal reporting. We document a conditional average lag of 28.5 months, with a fat-tail exceeding eight years. Overt unauthorized activity reduces the lag by 35.7%, whereas sophisticated fraud extends it by 58.6%. Using method of moments quantile regression, we reveal a strategic masking gradient: the impact of advisor experience more than doubles at the 90th percentile relative to the 10th. Product opacity acts as an expanding shield: insurance-linked disputes extend latency by by 61.9% at the 10th percentile and by 90.0% at the 90th percentile of the distribution. Finally, market volatility serves as an asymmetric catalyst for discovery: a doubling of the VIX reduces the lag by 21.1% for rapid-discovery cases, but only 7.9% for deeply concealed schemes. These strategically managed discovery delays allow bad types to persist across multiple market cycles.

Using theory and experiments, this paper shows that the difficulty of making tradeoffs offers a parsimonious explanation for a wide range of behavioral phenomena. We develop a model of imprecise comparisons applicable to multiattribute, lottery, and intertemporal choice, which formalizes the idea that comparisons are difficult when they involve pronounced tradeoffs. Our model rationalizes a range of documented regularities, such as context effects, preference reversals, apparent probability weighting and hyperbolic discounting, and generates novel implications for behavior. We assess the explanatory power of our model in a series of choice experiments. Our model explains a large share of the variation in choice inconsistency across problems, and we document that manipulating tradeoffs reverses classic behavioral regularities, in line with its predictions.