arXiv subjects

Liam Welsh

Publications and source records attributed to Liam Welsh.

4 recordsLinked to original sources

arXiv2025

Multi-Agent Reinforcement Learning for Greenhouse Gas Offset Credit Markets

Climate change is a major threat to the future of humanity, and its impacts are being intensified by excess man-made greenhouse gas emissions. One method governments can employ to control these emissions is to provide firms with emission limits and penalize any excess emissions above the limit. Excess emissions may also be offset by firms who choose to invest in carbon reducing and capturing projects. These projects generate offset credits which can be submitted to a regulating agency to offset a firm's excess emissions, or they can be traded with other firms. In this work, we characterize the finite-agent Nash equilibrium for offset credit markets. As computing Nash equilibria is an NP-hard problem, we utilize the modern reinforcement learning technique Nash-DQN to efficiently estimate the market's Nash equilibria. We demonstrate not only the validity of employing reinforcement learning methods applied to climate themed financial markets, but also the significant financial savings emitting firms may achieve when abiding by the Nash equilibria through numerical experiments.

q-fin.MF↗

arXiv2024

Nash Equilibria in Greenhouse Gas Offset Credit Markets

One approach to reducing greenhouse gas (GHG) emissions is to incentivize carbon capturing and carbon reducing projects while simultaneously penalising excess GHG output. In this work, we present a novel market framework and characterise the optimal behaviour of GHG offset credit (OC) market participants in both single-player and two-player settings. The single player setting is posed as an optimal stopping and control problem, while the two-player setting is posed as optimal stopping and mixed-Nash equilibria problem. We demonstrate the importance of acting optimally using numerical solutions and Monte Carlo simulations and explore the differences between the homogeneous and heterogeneous players. In both settings, we find that market participants benefit from optimal OC trading and OC generation.

q-fin.GN↗

arXiv2023

A generative approach to frame-level multi-competitor races

Multi-competitor races often feature complicated within-race strategies that are difficult to capture when training data on race outcome level data. Further, models which do not account for such strategic effects may suffer from confounded inferences and predictions. In this work we develop a general generative model for multi-competitor races which allows analysts to explicitly model certain strategic effects such as changing lanes or drafting and separate these impacts from competitor ability. The generative model allows one to simulate full races from any real or created starting position which opens new avenues for attributing value to within-race actions and to perform counter-factual analyses. This methodology is sufficiently general to apply to any track based multi-competitor races where both tracking data is available and competitor movement is well described by simultaneous forward and lateral movements. We apply this methodology to one-mile horse races using data provided by the New York Racing Association (NYRA) and the New York Thoroughbred Horsemen's Association (NYTHA) for the Big Data Derby 2022 Kaggle Competition. This data features granular tracking data for all horses at the frame-level (occurring at approximately 4hz). We demonstrate how this model can yield new inferences, such as the estimation of horse-specific speed profiles which vary over phases of the race, and examples of posterior predictive counterfactual simulations to answer questions of interest such as starting lane impacts on race outcomes.

stat.ME↗

arXiv2022

A Non-Parametric Bootstrap for Spectral Clustering

Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which can utilize the expectation-maximization (EM) algorithm. However, the EM algorithm falls victim to a number of issues, including convergence to sub-optimal solutions. We address this issue by developing two novel algorithms that incorporate the spectral decomposition of the data matrix and a non-parametric bootstrap sampling scheme. Simulations display the validity of our algorithms and demonstrate not only their flexibility, but also their computational efficiency and ability to avoid poor solutions when compared to other clustering algorithms for estimating finite mixture models. Our techniques are more consistent in their convergence when compared to other bootstrapped algorithms that fit finite mixture models.

stat.ML↗