Industry-academia ML collaborations routinely fail to launch -- not for scientific reasons, but because academics must publish while companies must protect models trained on proprietary data, and no standard contract framework resolves this tension. Because contracts are negotiated by legal departments alone, many apparent legal disputes are incentive misalignment problems that only scientists at the table can correctly diagnose. We propose PBOS (Protect-the-Business / Open-Source-the-Science), a community-adoptable contract template anchored to a single technically-grounded boundary: pre-training artifacts (architectures, training code, benchmarks, untrained weights) are open science; post-training artifacts (weights trained on proprietary data) are business IP. This boundary is technically meaningful, legally clean, and auditable -- and could not have been drawn correctly without scientists at the negotiating table. We argue the ML community should adopt PBOS as its default contract for such collaborations.

Generating synthetic data for financial time series poses challenges, especially considering their non-stationary nature. Traditional statistical time series models normally assume weak stationarity. However, this assumption can constrain their effectiveness. Deep learning models, particularly Generative Adversarial Networks (GANs), have exhibited considerable potential in emulating complex probability distributions. GANs employ a generator-discriminator framework, where the generator creates data samples, while the discriminator distinguishes real from generated data. In this research, we introduce the Sig-Graph GAN model, which integrates the time-series signature, offering a structured summary of its temporal evolution; the Long Short-Term Memory network, capturing its inherent autoregressive structure; and Graph Neural Networks (GNNs), leveraging geometric patterns within the time-series data. To employ GNNs optimally, we use the visibility graph algorithm to derive a graph-based representation of the underlying time series. Numerical evaluations demonstrate that the Sig-Graph GAN model outperforms baseline methods in replicating the distribution of logarithmic returns across different stock exchanges. The integration of the graph structure with the autoregressive component effectively captures both geometric and temporal patterns embedded in time-series data. This research advances the field of GAN models for time series by introducing a model capable of leveraging both autoregressive properties and geometric structures for synthetic data generation.

The emergence of large language models (LLMs) has spurred economists to study how humans and LLMs behave in strategic settings. We organized a series of round-robin tournaments in the Colonel Blotto game. This game attracts game theorists' attention due to high-dimensional action space and the absence of pure strategy Nash equilibria. In the first tournament, more than 200 human participants competed against one another. In the second tournament, several popular LLMs were invited to submit strategies. In the third tournament, we matched the number of LLM strategies to the number submitted by humans. We find that humans more often employ better-calibrated intermediate-level allocation heuristics and outperform the simpler, more stereotyped strategies submitted by LLMs. Strategic sophistication is key to success if and only if the necessary level of reasoning depth is reached, while lower and higher levels of reasoning offer no clear advantage over the primitive strategies. Among humans, field of study weakly predicts success: participants with STEM backgrounds perform better in the first tournament. Surprisingly, humans almost do not adjust their strategies across tournaments with different sets of opponents. This result suggests that humans base their choices primarily on the game's rules rather than on the identity of their opponents, treating LLMs much like human competitors.

In this paper, we investigate whether deep reinforcement-learning agents interacting in a shared optimal-execution environment can sustain supra-competitive outcomes, in the sense of achieving lower implementation shortfalls than the relevant game-theoretical competitive benchmark. We study a two-agent Almgren-Chriss liquidation game and examine how learned behavior depends on intra-episode environment feedback, the ability to interpret the mid-price and the agent's knoledge of the past. We first use ex-ante schedule-learning agents to remove intra-episode feedback and isolate what can arise when agents commit to complete liquidation trajectories before execution begins. We then allow agents to condition on the evolving state using a variety of DDQN architectures. We find that, when agents are given access to intra-episode history, especially recent prices and own past actions, supra-competitive outcomes become substantially more frequent and more persistent. These findings indicate that supra-competitive behavior in this execution game is driven not by multi-agent learning or by current price observation alone, but by feedback, memory, and state-contingent interaction along the realized execution path.

We study Stackelberg Equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria are characterized as follows: In equilibrium, the optimal indemnity function exhibits a layer-type structure, providing full insurance over any loss layer on which the policyholder is more pessimistic than the insurer's pricing functional about tail losses; and no insurance coverage over loss layers on which the policyholder is less pessimistic than the insurer's pricing functional about tail losses. In equilibrium, the optimal pricing distortion function is determined by the policyholder's degree of risk aversion, whereby prices never exceed the policyholder's marginal willingness to insure tail losses. Moreover, we show that both the insurance coverage and the insurer's expected profit increase with the policyholder's degree of risk aversion. Additionally, and echoing recent work in the literature, we show that equilibrium contracts are Pareto efficient, but they do not induce a welfare gain to the policyholder. Conversely, any Pareto-optimal contract that leaves no welfare gain to the policyholder can be obtained as an equilibrium contract. Finally, we consider a few examples of interest that recover some existing results in the literature as special cases of our analysis.

While traditional equity factor investing relies heavily on slow-moving fundamental accounting metrics, these models frequently suffer from factor crowding and miss real-time, sentiment-driven market dislocations. This study explores how institutional investors can leverage a high-dimensional library of 191 short-term, trading-based signals, originally developed for the retail-heavy Chinese A-share market, to enhance alpha generation within the highly institutionalized U.S. S&P 500 universe from 2002 to 2022. Utilizing a robust double-selection LASSO framework to control for 151 established fundamental factors, we isolate 17 distinct price-volume and microstructural signals that capture significant, non-redundant risk premiums. Our empirical evidence demonstrates that these fast trading signals capture universal behavioral dynamics that do not dilute over a monthly rebalancing horizon. Integrating these short-term behavioral footprints with slow fundamental data offers a powerful dual-horizon framework to mitigate model misspecification risk and enhance large-cap portfolio diversification.

We study relationships between dynamic programs by applying conjugacy methods from dynamical systems theory. When two dynamic programs are connected by an order isomorphism, we show that optimality properties transmit from one formulation to the other. We apply these results to Epstein--Zin preferences with time preference shocks, obtaining a sharp characterization of when optimality holds. We also show that multiplicative Kreps--Porteus preferences and risk-sensitive preferences are isomorphic, so that well-known results for the latter carry over to the former. Finally, we demonstrate how isomorphic transformations can improve the numerical accuracy of value function approximations, with gains of two orders of magnitude in a multisector real business cycle model.

We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which ambiguity is captured by penalized worst-case expectations over alternative transition laws. Imposing time consistency then yields a convex monotone semigroup on bounded continuous payoff functions, and this semigroup represents the associated dynamic risk measure. The semigroup is uniquely characterized by its risk generator. Under a lower bound on the family of penalties in terms of suitable optimal transport costs relative to the reference laws, we identify the generator on smooth test functions. For optimal transport bounds with linear small-time scaling, this produces a first-order, drift-type correction given by a convex Hamiltonian acting on the gradient. Under martingale transport constraints and a different scaling, however, the leading correction is genuinely of second order and is described by a convex monotone functional acting on the Hessian. We illustrate both regimes for Wasserstein and martingale Wasserstein penalizations and derive explicit formulas via convex conjugates of the underlying transport costs. The associated dynamic risk measures admit stochastic control representations in which the control acts on the drift in the first-order case and on the volatility in the second-order case.

This paper studies empirical deep hedging for S&P 500 index options under a local downside-shortfall reward. It moves beyond performance comparison by asking what the learned hedge does, when it fails, and whether it can be made auditable. TD3 agents are compared with a daily-updated Black-Scholes delta hedge on the same option episodes. In walk-forward tests from 2015 to 2023, the agents usually learn a systematic delta haircut relative to Black-Scholes. The correction is explained by spot-implied-volatility co-movement and often improves accumulated reward and terminal downside variance, but it is regime-fragile: 2022 exposes losses in adverse daily states, while 2023 shows that underhedging can raise ordinary variance when option P&L is spot-dominated and the volatility channel is unusually weak. Symbolic regression distills the neural policies into compact formulas that can be traded out of sample; these formulas preserve much of the reward, downside-variance, and CVaR advantage over Black-Scholes, and sometimes sharpen it, but inherit the same fragility in difficult regimes.

The impact of rising consumption on wealth inequality remains an open question. Here we revisit and extend the Social Architecture of Capitalism agent-based model proposed by Ian Wright, which reproduces stylized facts of wealth and income distributions. In a previous study, we demonstrated that the macroscopic behavior of the model is predominantly governed by a single dimensionless parameter, the ratio between average wealth per capita and mean salary, denoted by R. The shape of the wealth distribution, the emergence of a two-class structure, and the level of inequality - summarized by the Gini index - were found to depend mainly on R, with inequality increasing as R increases. In the present work, we examine the robustness of this result by relaxing some simplifying assumptions of the model. We first allow transactions such as purchases, salary payments, and revenue collections to occur with different frequencies, reflecting the heterogeneous temporal dynamics of real economies. We then impose limits on the maximum fractions of wealth that agents can spend or collect at each step, constraining the amplitude of individual transactions. We find that the dependence of the inequality on R remains qualitatively robust, although the detailed distribution patterns are affected by relative frequencies and transaction limits. Finally, we analyze a further variant of the model with adaptive wages emerging endogenously from the dynamics, showing that self-organized labor-market feedback can either stabilize or amplify inequality depending on macroeconomic conditions.

This paper investigates how productivity dispersion relates to input misallocation in European manufacturing. The model features staggered productivity shocks that create wedges between anticipated and realized productivity for any production input. Using European firm-level data from 2001-2017, I show that, under the maintained model, shocks realized after inputs are committed are the largest contributor to marginal revenue product dispersion for every input, accounting for 75% of the variance for materials, 37% for labor, and 18% for capital. These results are consistent with input misallocation in European manufacturing reflecting post-commitment productivity shocks more than persistent heterogeneity across firms.

We study the system of heterogeneous interbank lending and borrowing based on the relative average of log-capitalization given by the linear combination of the average within groups and the ensemble average and describe the evolution of log-capitalization by a system of coupled diffusions. The model incorporates a game feature with homogeneity within groups and heterogeneity between groups where banks search for the optimal lending or borrowing strategies through minimizing the heterogeneous linear quadratic costs in order to avoid to approach the default barrier. Due to the complicity of the lending and borrowing system, the closed-loop Nash equilibria and the open-loop Nash equilibria are both driven by the coupled Riccati equations. The existence of the equilibria in the two-group case where the number of banks are sufficiently large is guaranteed by the solvability for the coupled Riccati equations as the number of banks goes to infinity in each group. The equilibria are consisted of the mean-reverting term identical to the one group game and the group average owing to heterogeneity. In addition, the corresponding heterogeneous mean filed game with the arbitrary number of groups is also discussed. The existence of the $ε$-Nash equilibrium in the general $d$ heterogeneous groups is also verified. Finally, in the financial implication, we observe the Nash equilibria governed by the mean-reverting term and the linear combination of the ensemble averages of individual groups and study the influence of the relative parameters on the liquidity rate through the numerical analysis.

We propose a simple model of the banking system incorporating a game feature where the evolution of monetary reserve is modeled as a system of coupled Feller diffusions. The Markov Nash equilibrium generated through minimizing the linear quadratic cost subject to Cox-Ingersoll-Ross type processes creates liquidity and deposit rate. The adding liquidity leads to a flocking effect but the deposit rate diminishes the growth rate of the total monetary reserve causing a large number of bank defaults. In addition, the corresponding Mean Field Game and the infinite time horizon stochastic game with the discount factor are also discussed.