Nash equilibrium serves as a fundamental mathematical tool in economics and game theory. However, it classically assumes knowledge of player utilities, whereas economics generally regards preferences as more fundamental. To leverage equilibrium analysis in strategic scenarios, one must first elicit numerical utilities consistent with player preferences, a delicate and time-consuming process. In this work, we forgo precise utilities and generalize the Nash equilibrium to a setting where we only assume a player is capable of providing an ordinal ranking of their actions within the context of other players' joint actions. The key technical challenge is to rethink the definition of a best-response. While the classical definition identifies actions maximizing expected payoff, we naturally look towards social choice theory for how to aggregate preferences to identify the most preferred actions. We define this generalized notion of a context-ordinal Nash equilibrium, establish its existence under mild conditions on aggregation methods, introduce notions of regularization, approximation, and regret, explore complexity for simple settings, and develop learning rules for computing such equilibria. In doing so, we provide a generalization of Nash equilibrium and demonstrate its direct applicability to elicited preferences in human experiments.

This paper refutes the claim that the expected rate of return of the underlying asset plays no role in the Black-Scholes-Merton option pricing model.

We show that the leading bubble test suffers severe size distortion when fundamentals incorporate general-purpose technology adoption. Embedding a hump-shaped technology shock in the Campbell-Shiller present-value model, we prove that the fundamental price becomes locally explosive during adoption, contaminating the test's limit distribution with a non-centrality parameter proportional to the shock's peak. We propose a fundamental-versus-speculative decomposition that projects prices onto observable technology proxies and applies the test to the residual. Empirically, the decomposition eliminates evidence of speculation in the 2020-2025 AI rally while confirming a speculative peak confined to December 1999-March 2000 in the dot-com episode.

As generative artificial intelligence (GenAI) automates coding tasks and expands access to technical resources, this paper examines how GenAI-enabled coding automation, colloquially known as "vibecoding," affects digital entrepreneurial entry and venture performance. We exploit ex-ante variation in ventures' exposure to vibecoding based on the product characteristics of their initial launches and estimate difference-in-differences models around the diffusion of GenAI coding tools. Vibecoding increases first-time launches and shortens time to launch, but economically viable entry rises only where vibecoding augments, rather than fully automates, product development. In these partially exposed product segments, viable entry increases by 11%, driven entirely by ventures founded by individuals with STEM education or work experience, especially those whose most recent employment was outside middle management. Among ventures launched before GenAI became widely accessible, performance gains similarly concentrate among partially exposed ventures with engineering-intensive initial teams. Together, these results suggest that GenAI-enabled coding automation does not eliminate the value of technical expertise. Instead, vibecoding creates the greatest value when it complements internal engineering capabilities, allowing ventures to delegate lower-level coding tasks to GenAI while shifting human effort toward higher-level problem solving and dynamic adaptation.

In this paper we study the short-maturity asymptotics of up-and-in barrier options under a broad class of stochastic volatility models. Our approach uses Malliavin calculus techniques, typically used for linear stochastic partial differential equations, to analyse the law of the supremum of the log-price process. We derive a concentration inequality and explicit bounds on the density of the supremum in terms of the time to maturity. These results yield an upper bound on the asymptotic decay rate of up-and-in barrier option prices as maturity vanishes. We further demonstrate the applicability of our framework to the rough Bergomi model and validate the theoretical results with numerical experiments.

We study two complementary methodologies for calibrating implied volatility surfaces: analytical approximations and data-driven models based on rough path theory. On the analytical side, we revisit a second-order asymptotic expansion for the Heston model, and we propose a new, VIX-based calibration scheme for the rough Bergomi model. Both methods yield highly accurate and computationally efficient calibration formulas when the underlying dynamics are well specified. In parallel, we develop a signature-based approach in which volatility is represented as a linear functional of the truncated signature of a primary stochastic process, providing a flexible and model-agnostic alternative. Our numerical experiments compare the two approaches across both Markovian and non-Markovian settings. In the Heston case, signature-based models achieve a level of accuracy comparable to analytical expansions. In the rough Bergomi setting, using a fractional Brownian motion as the primary process, the signature approach continues to perform strongly and in some cases improves upon the Markovian specification, reflecting its ability to capture more complex temporal dependencies. Overall, the results illustrate that analytical methods are highly effective when the model is correctly specified, while signature-based methods offer a robust and flexible framework for calibration across a wider range of volatility dynamics.

The disposition effect describes investors' irrational behavior of selling profitable assets too soon while holding onto losing assets for too long. This study examines the impact of transparency at the firm level on the disposition effect of individual investors who hold that company's stock. Our results show that an increase in corporate transparency significantly reduces the disposition effect. Further analysis reveals that for companies with greater transparency, when the held stock is profitable, investors' confidence in holding it increases, leading to a reduced bias toward selling profitable stocks. When the stock is held at a loss, investors' confidence in holding it weakens, but they often perceive the loss as temporary and maintain confidence in the company's long-term prospects, thus exacerbating the bias toward holding losing stocks. The effect of increased transparency on the selling behavior of profitable stocks is greater than its effect on the selling behavior of losing stocks. Overall, an increase in corporate transparency significantly reduces the disposition effect.

Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional difficulty is summarizing the estimated evolving dependence structure for downstream decision-making tasks. We propose a Bayesian approach based on a low-rank factor representation, with latent states evolving under a dynamic shrinkage prior and observation errors following a multivariate factor stochastic volatility model. This specification allows locally adaptive regularization of the estimated correlation structure over time and informative uncertainty quantification. We establish, to our knowledge, a first-of-its-kind posterior contraction result for dynamically regularized Bayesian models, showing contraction around the true model parameters at an explicit rate under averaged Hellinger distance. To summarize the estimated correlation matrices, we build on the information-theoretic concept of total correlation to obtain a scalar measure of cross-sectional dependence. Simulation studies show improved accuracy and responsiveness relative to competing methods in a range of challenging scenarios. We then apply our method to monitoring the correlation evolution of equity portfolios during periods of financial market stress, providing an ex post framework for assessing the changing benefits of diversification in backtesting analyses.

System dynamics is a methodology that is widely used in many academic fields. It explains the behavior of social and economic systems with models that capture complex causality and feedback effects. This 'practice paper' discusses the opportunities and barriers for introducing feedback thinking and system dynamics models in the economics curriculum. We start by providing a pricing feedback model that illustrates some of the benefits that system dynamics can provide in enhancing economics education. Then we summarize the experiences of each of the authors in teaching system dynamics on economics educational programs. This includes different approaches to teaching economics with system dynamics that depend on the learning objectives, the preparation of students, and the background of the instructor. We also develop a four-level course hierarchy for using system dynamics in economics teaching. We then point out the tradeoffs that instructors must consider as they introduce new pedagogies for delivering economics material. Finally, we provide some concluding comments with some suggestions for future work. The expected audiences for this paper are instructors as well as graduate students who are considering academia as a profession.

In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an unknown, time-varying exercise boundary. The Heston model is one of the most popular ways to model real market behavior because it allows volatility to change over time. However, unlike European options, there is no closed-form solution for American options under the Heston model, so we have to use numerical methods. In this paper, we propose a novel approach to solving the stochastic Heston partial differential equation for American options, using coupled physics-informed neural networks (PINNs) to predict both the option price and the free boundary, while employing curriculum learning and adaptive resampling to stabilize model training. Our work builds on recent deep learning methods but introduces a more effective training strategy to address the limitations of these approaches. The numerical results demonstrate the effectiveness of the proposed learning framework, providing a robust and efficient alternative to pricing American options, enabling rapid inference and accurate estimation under stochastic volatility.

According to the United Nations Office for Disaster Risk Reduction (2025), the average annual cost of natural catastrophes increased from 70--80 billion USD between 1970 and 2000 to 180--200 billion USD between 2001 and 2020. Reports from organizations such as the IFOA and the WWF highlight the need for the insurance sector to adapt to this rapidly evolving context by developing medium- to long-term strategies that go beyond the one-year horizon of prudential regulations such as Solvency II. This paper introduces an artificial intelligence framework based on Conditional Generative Adversarial Networks (Conditional GANs) to generate future spatio-temporal trajectories of climatic indices. The approach focuses on the Soil Wetness Index (SWI), a key indicator used in France to assess drought severity. Drought accounts for approximately 30% of the indemnities paid under the French natural catastrophe insurance scheme. The proposed model, SwiGAN, simulates plausible drought propagation patterns up to 2050 for a region of France particularly exposed to this hazard. By generating realistic sequences of SWI maps, SwiGAN provides insights into drought dynamics under climate change scenarios and supports the design of adaptive risk management and insurance strategies. The methodology is also generalizable to other climate-related perils and actuarial applications such as economic scenario generation.

Barrier derivatives depend on extrema and first-passage events and are therefore highly sensitive to volatility dynamics -- especially to the instantaneous return-volatility correlation $ρ$, often called ``leverage''. This sensitivity makes accurate and fast pricing under realistic stochastic-volatility specifications difficult: two-dimensional PDE solvers are expensive inside calibration loops, while Monte Carlo methods converge slowly when barrier hits are rare and discretely monitored. In equity markets in particular, the pronounced implied-volatility skew motivates factoring in a negative return-volatility correlation. We study a class of continuous-path stochastic-clock volatility models in which the log-price is represented as a Brownian motion run on a random increasing clock. In the baseline independent-clock case (ρ=0), a broad family of barrier-relevant objects-maximum distributions, survival probabilities, and killed joint laws-reduces to one-dimensional quantities determined by the Laplace transform of the terminal clock. This yields transform-only pricing formulas for single- and double-barrier contracts that are fast and numerically stable once the clock transform is available, notably for affine and quadratic clocks. To incorporate leverage without forfeiting tractability, we develop a systematic small-ρexpansion around the ρ=0 backbone. The expansion produces a hierarchy of forced problems whose forcing terms are semi-analytic and computable from baseline barrier objects. We provide two implementable leverage-correction routes\,: forced PDEs and a Duhamel-type Monte Carlo representation, and we show how Pad{é} acceleration can extend practical accuracy to equity-like correlations. Calibration then proceeds by\,: (i) fitting clock parameters from vanillas using only one-dimensional transforms, (ii) precomputing the ρ=0 barrier backbone once, and (iii) iterating on ρ(and any remaining parameters) using the fast semi-analytic corrections-optionally Pad{é}-accelerated-inside a standard least-squares loop.

The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control problem is high-dimensional. We propose a backward actor-critic stochastic policy gradient scheme tailored to this setting. The method combines a discrete dynamic programming principle with Proximal Policy Optimization and shallow neural-network approximations of both the value function and the control policy. A key ingredient is the policy parameterization: continuous controls are represented through a squashed Gaussian policy built on a C-vine representation of correlation matrices, which enforces positive semidefiniteness by construction. Numerical experiments on a range of multidimensional derivatives show that the method yields accurate prices, remains computationally efficient, and compares favorably with existing Monte Carlo and machine-learning-based benchmarks for robust pricing in the Uncertain Volatility Model.

We develop a stochastic game-theoretic model for intraday dispatch of grid-scale battery energy storage systems (BESSs). We assume that each BESS operator competitively manages her state-of-charge to maximize energy arbitrage revenues, driven by the endogenized electricity price that depends on the sum of the charging rates. We characterize the Nash equilibrium of the resulting finite-player linear-quadratic differential game with a shared stochastic driver, obtaining semi-explicit representations of equilibrium feedback controls and equilibrium prices both in the general heterogeneous and the simplified homogeneous BESS setting, via a system of Riccati equations. We then analyze competitive effects, including the marginal externality of additional BESS entering the market, the benefit of coordination and the corresponding market power of large operators, and supply effects from hybrid-type BESSs. We further study the asymptotic regime as the number of agents grows large. Our model provides a quantitative testbed to study the impact of decentralized BESS deployment on the grid and the resulting reduction in daily price spreads.

USDC and USDT are the dominant stablecoins pegged to \$1 with a total market capitalization of over \$300B and rising. Stablecoins make dollar value globally accessible with secure transfer and settlement. Yet in practice, these stablecoins experience periods of stress and de-pegging from their \$1 target, posing significant systemic risks. The behavior of market participants during these stress events and the collective actions that either restore or break the peg are not well understood. This paper addresses the question: who restores the peg?. We develop a dynamic, agent-based mean-field game framework for fiat-collateralized stablecoins, in which a large population of arbitrageurs and retail traders strategically interact across primary and secondary markets during a de-peg episode. The key advantage of this equilibrium formulation is that it endogenously maps market frictions into a market-clearing price path and implied net order flows, allowing us to attribute peg-reverting pressure by channel and to stress-test when a given infrastructure becomes insufficient for recovery. Using three historical de-peg events, we show that the calibrated equilibrium reproduces observed recovery half-lives and yields an order flow decomposition in which system-wide stress is predominantly stabilized by primary-market arbitrage. Finally, a quantitative sensitivity analysis identifies a non-linear breakdown threshold, beyond which a de-peg becomes markedly slower to reverse.

Diffusion Probabilistic Model (DDPM) for generating one-day-ahead arbitrage-free implied volatility surfaces. To capture the path-dependent nature of volatility dynamics, we condition our model on a set of market variables, including exponentially weighted moving averages (EWMAs) of historical vol-surfaces, returns and squared returns of the underlying asset, and scalar risk indicators associated with the underlying asset. A key challenge is that historical data often contains arbitrage opportunities in the earlier dataset for training, which conflicts with the goal of generating arbitrage-free surfaces. We address this by using a parameter-free weighting scheme based on the signal-to-noise ratio (SNR) to incorporate the arbitrage penalty into the loss function. The scheme dynamically adjusts the penalty strength across the diffusion process. Through numerical experiments using market data, we demonstrate the superior performance of our proposed model in volatility forecasting compared to existing approaches.

The rapid growth of digital shopping channels has prompted many traditional retailers to invest in e-commerce websites and mobile apps. While prior literature shows that multichannel customers are more valuable, it overlooks how the motive for adopting a new channel shapes post-adoption behavior. Using transaction-level data from a major Brazilian pet supplies retailer, we study offline-only consumers who adopt online shopping via four distinct pathways: organic adoption, the COVID-19 pandemic, Black Friday promotions, and a loyalty program. We examine how these pathways affect post-adoption spend, profitability, and channel usage using consumer-level panel data and difference-in-differences estimates. We find that all adopters increase spending relative to offline-only consumers, but their post-adoption behaviors differ systematically by adoption motive. Promotion-driven adopters engage in forward buying and exhibit lower subsequent profitability, whereas COVID-19 adopters display stronger offline persistence consistent with consumer inertia and habit theory. Our findings have important managerial implications: firms should design promotions that discourage stockpiling, reinforce habits among customers pushed online by external shocks, and explicitly account for heterogeneity in channel adoption motives when forecasting customer lifetime value and assessing the breakeven and ROI of promotions designed to induce the adoption of new channels.

We propose a methodology to estimate the market value of pharmaceutical drugs. Our approach combines the event study method with a discounted cash flow model that infers drug values from stock market responses to drug development announcements. We estimate the average value of a drug developed by small firms (those below the 95th percentile of market capitalization) to be \$2.16 billion. At the preclinical stage, the risk-adjusted and present discounted average net value of drugs is \$50 million. Leveraging these estimates, we also determine the expected drug development cost at the start of the discovery stage to be \$38 million. We estimate values and costs for several therapeutic areas (e.g., neoplasm, infections) and explore applying these estimates to design policies that support drug development through drug buyouts and targeted preclinical interventions.

We study actual bidding behavior when a new auction format gets introduced into the marketplace. More specifically, we investigate this question using a novel dataset on internet display advertising auctions that exploits a staggered adoption by different publishers (sellers) of first-price auctions (FPAs), instead of the traditional second-price auctions (SPAs). We analyze the auction format change using difference-in-differences regressions and a synthetic difference-in-differences estimator, which better handles pre-trends. The results show that revenue per sold impression (price) jumps considerably for treated publishers relative to control publishers, with increases ranging from 25% to 75% of the pre-treatment price level of the treated group. Moreover, for later auction format changes, the increase in price levels under FPAs relative to those under SPAs tends to dissipate over time, reminiscent of the revenue equivalence theorem, although the extent of this reversion depends on the specification. We view these results as suggestive of initially insufficient bid shading following the format change, as opposed to an immediate transition to a new Bayesian Nash equilibrium, with prices tending to decline in several specifications in a manner consistent with gradual adjustment in bidding behavior as bidders learn to shade their bids. Our work constitutes one of the first field studies on bidders'responses to auction format changes, providing an important complement to theoretical model predictions. As such, it provides valuable information to auction designers when considering the implementation of different formats.