Given ongoing, human-induced, loss of wild species we propose the Target and Cost Analysis (TCA) approach as a means of incorporating biodiversity within government appraisals of public spending. Influenced by how carbon is priced in countries around the world, the resulting biodiversity shadow price reflects the marginal cost of meeting government targets while avoiding disagreements on the use of willingness to pay measures to value biodiversity. Examples of how to operationalize TCA are developed at different scales and for alternative biodiversity metrics, including extinction risk for Europe and species richness in the UK. Pricing biodiversity according to agreed targets allows trade-offs with other wellbeing-enhancing uses of public funds to be sensibly undertaken without jeopardizing those targets, and is compatible with international guidelines on Cost Benefit Analysis.

Learning profitable intraday trading policies from financial time series is challenging due to heavy noise, non-stationarity, and strong cross-sectional dependence among related assets. We propose \emph{WaveLSFormer}, a learnable wavelet-based long-short Transformer that jointly performs multi-scale decomposition and return-oriented decision learning. Specifically, a learnable wavelet front-end generates low-/high-frequency components via an end-to-end trained filter bank, guided by spectral regularizers that encourage stable and well-separated frequency bands. To fuse multi-scale information, we introduce a low-guided high-frequency injection (LGHI) module that refines low-frequency representations with high-frequency cues while controlling training stability. The model outputs a portfolio of long/short positions that is rescaled to satisfy a fixed risk budget, and is optimized directly with a trading objective and risk-aware regularization. Extensive experiments on five years of hourly data across six industry groups, evaluated over ten random seeds, demonstrate that WaveLSFormer consistently outperforms MLP, LSTM and Transformer backbones, with and without fixed discrete wavelet front-ends. On average in all industries, WaveLSFormer achieves a cumulative overall strategy return of $0.607 \pm 0.045$ and a Sharpe ratio of $2.157 \pm 0.166$, substantially improving both profitability and risk-adjusted returns over the strongest baselines.

We propose Mixed-Panels-Transformer Encoder (MPTE), a novel framework for estimating factor models in panel datasets with mixed frequencies and nonlinear signals. Traditional factor models rely on linear signal extraction and require homogeneous sampling frequencies, limiting their applicability to modern high-dimensional datasets where variables are observed at different temporal resolutions. Our approach leverages Transformer-style attention mechanisms to enable context-aware signal construction through flexible, data-dependent weighting schemes that replace fixed linear combinations with adaptive reweighting based on similarity and relevance. We extend classical principal component analysis (PCA) to accommodate general temporal and cross-sectional attention matrices, allowing the model to learn how to aggregate information across frequencies without manual alignment or pre-specified weights. For linear activation functions, we establish consistency and asymptotic normality of factor and loading estimators, showing that our framework nests Target PCA as a special case while providing efficiency gains through transfer learning across auxiliary datasets. The nonlinear extension uses a Transformer architecture to capture complex hierarchical interactions while preserving the theoretical foundations. In simulations, MPTE demonstrates superior performance in nonlinear environments, and in an empirical application to 13 macroeconomic forecasting targets using a selected set of 48 monthly and quarterly series from the FRED-MD and FRED-QD databases, our method achieves competitive performance against established benchmarks. We further analyze attention patterns and systematically ablate model components to assess variable importance and temporal dependence. The resulting patterns highlight which indicators and horizons are most influential for forecasting.

Deep learning models are effective for sequential data modeling, yet commonly used activation functions such as ReLU, LeakyReLU, and PReLU often exhibit gradient instability when applied to noisy, non-stationary financial time series. This study introduces BrownianReLU, a stochastic activation function induced by Brownian motion that enhances gradient propagation and learning stability in Long Short-Term Memory (LSTM) networks. Using Monte Carlo simulation, BrownianReLU provides a smooth, adaptive response for negative inputs, mitigating the dying ReLU problem. The proposed activation is evaluated on financial time series from Apple, GCB, and the S&P 500, as well as LendingClub loan data for classification. Results show consistently lower Mean Squared Error and higher $R^2$ values, indicating improved predictive accuracy and generalization. Although ROC-AUC metric is limited in classification tasks, activation choice significantly affects the trade-off between accuracy and sensitivity, with Brownian ReLU and the selected activation functions yielding practically meaningful performance.

Cyber risk has become a critical financial threat in today's interconnected digital economy. This paper introduces a cyber-risk management framework for networked digital systems that combines the strategic behavior of players with contagion dynamics within a security game. We address the problem of optimally allocating cybersecurity resources across a network, focusing on the heterogeneous valuations of nodes by attackers and defenders, some areas may be of high interest to the attacker, while others are prioritized by the defender. We explore how this asymmetry drives attack and defense strategies and shapes the system's overall resilience. We extend a method to determine optimal resource allocation based on simple network metrics weighted by the defender's and attacker's risk profiles. We further propose risk measures based on contagion paths and analyze how propagation dynamics influence optimal defense strategies. Numerical experiments explore risk versus cost efficient frontiers varying network topologies and risk profiles, revealing patterns of resource allocation and cyber deception effects. These findings provide actionable insights for designing resilient digital infrastructures and mitigating systemic cyber risk.

Compositional time series, vectors of proportions summing to unity observed over time, frequently exhibit structural breaks due to external shocks, policy changes, or market disruptions. Standard methods either ignore such breaks or handle them through ad-hoc dummy variables that cannot extrapolate beyond the estimation sample. We develop a Bayesian Dirichlet ARMA model augmented with a directional-shift intervention mechanism that captures structural breaks through three interpretable parameters: a unit direction vector specifying which components gain or lose share, an amplitude controlling the magnitude of redistribution, and a logistic gate governing the timing and speed of transition. The model preserves compositional constraints by construction, maintains innovation-form DARMA dynamics for short-run dependence, and produces coherent probabilistic forecasts during and after structural breaks. We establish that the directional shift corresponds to geodesic motion on the simplex and is invariant to the choice of ILR basis. A comprehensive simulation study with 400 fits across 8 scenarios demonstrates that when the shift direction is correctly identified (77.5% of cases), amplitude and timing parameters are recovered with near-zero bias, and credible intervals for the mean composition achieve nominal 80% coverage; we address the sign identification challenge through a hemisphere constraint. An empirical application to fee recognition lead-time distributions during COVID-19 compares baseline, fixed-effects, and intervention specifications in rolling forecast evaluation, demonstrating the intervention model's superior point accuracy (Aitchison distance 0.83 vs. 0.90) and calibration (87% vs. 71% coverage) during structural transitions.

This study examines how multinational enterprises structure ownership chains to coordinate subsidiaries across multiple national borders. Using a unique global dataset, we first document key stylized facts: 54% of subsidiaries are controlled through indirect ownership, and ownership chains can span up to seven countries. In particular, we find that subsidiaries further down the control hierarchy tend to be more geographically distant from the parent and operate in different time zones. This suggests that the ease of communication along ownership chains is a critical determinant of their structure. On the other hand, tax optimization strategies are not correlated with locations along ownership chains. Motivated by previous findings, we develop a location choice model in which parent firms compete for corporate control of final subsidiaries, but monitoring is costly, and they can delegate control to an intermediate affiliate in another jurisdiction. The model generates a two-stage empirical strategy: (i) a trilateral equation that determines the location of an intermediate affiliate conditional on the location of final subsidiaries; and (ii) a bilateral equation that predicts the location of final investment. Our empirical estimates confirm that the ease of communication at the country level has a significant influence on the location decisions of affiliates along ownership chains. Our findings underscore the importance of communication frictions in shaping global corporate structures, and provide new insights into the geography of multinational ownership networks.

This paper addresses the problem of robust option pricing within the framework of Vectorial Martingale Optimal Transport (VMOT). We investigate the geometry of VMOT solutions for $N$-period market models and demonstrate that, when the number of underlying assets is $d=2$ and the payoff is sub- or supermodular, the extremal model reduces to a single-factor structure in the first period. This structural result allows for a significant dimension reduction, transforming the problem into a more tractable format. We prove that this reduction is specific to the two-asset case and provide counterexamples showing it generally fails for $d \geq 3$. Finally, we exploit this monotonicity to develop a reduced-dimension Sinkhorn algorithm. Numerical experiments demonstrate that this structure-preserving approach reduces computational time by approximately 99\% compared to standard methods while improving accuracy.

The declining provision of inertia by synchronous generators in modern power systems necessitates aggregating distributed energy resources (DERs) into virtual power plants (VPPs) to unlock their potential in delivering inertia and primary frequency response (IPFR) through ancillary service markets. To facilitate DER participation in the IPFR market, this paper proposes an aggregation model and market mechanism for VPPs participating in IPFR. First, an energy-reserve-IPFR market framework is developed, in which a VPP acts as an intermediary to coordinate heterogeneous DERs. Second, by taking into account the delay associated with inertial response, an optimization-based VPP aggregation method is introduced to encapsulate the IPFR process involving a variety of DERs. Third, an energy-reserve-IPFR market mechanism with VPP participation is introduced, aiming to minimize social costs, where stochastic deviations of renewable energy generation are explicitly modeled through chance-constrained reformulations, ensuring that the cleared energy, reserve, and IPFR schedules remain secure against forecast errors. Case studies on IEEE 30-bus and IEEE 118-bus systems show that the nadir and quasi-steady-state frequencies are reproduced by the VPP aggregation model with a mean absolute percentage error <= 0.03%, and the proposed market mechanism with VPP participation reduces the total system cost by approximately 40% and increases the net profit by about 30%.

I study how firms adjust to temporary disruptions in international trade relationships organized through relational contracts. I exploit an extreme, plausibly exogenous weather shock during the 2010-11 La Niña season that restricted Colombian flower exporters' access to cargo terminals. Using transaction-level data from the Colombian-U.S. flower trade, I show that importers with less-exposed supplier portfolios are less likely to terminate disrupted relationships, instead tolerating shipment delays. In contrast, firms facing greater exposure experience higher partner turnover and are more likely to exit the market, with exit accounting for a substantial share of relationship separations. These findings demonstrate that idiosyncratic shocks to buyer-seller relationships can propagate into persistent changes in firms' trading portfolios.

Detecting fraudulent auto-insurance claims remains a challenging classification problem, largely due to the extreme imbalance between legitimate and fraudulent cases. Standard learning algorithms tend to overfit to the majority class, resulting in poor detection of economically significant minority events. This paper proposes a structured three-stage training framework that integrates a convex surrogate of focal loss for stable initialization, a controlled non-convex intermediate loss to improve feature discrimination, and the standard focal loss to refine minority-class sensitivity. We derive conditions under which the surrogate retains convexity in the prediction space and show how this facilitates more reliable optimization when combined with deep sequential models. Using a proprietary auto-insurance dataset, the proposed method improves minority-class F1-scores and AUC relative to conventional focal-loss training and resampling baselines. The approach also provides interpretable feature-attribution patterns through SHAP analysis, offering transparency for actuarial and fraud-analytics applications.