In this paper, I introduce a new emissions trading system (ETS) design to address the problems with existing ETSs and carbon taxes. First, existing ETS designs inhibit emissions but do not constrain warming to any set level. Existing ETSs have the indirect objective of reducing emissions instead of directly reducing warming. Even a global mechanism using an existing ETS cannot guarantee a particular warming path. Part 1: A Price on Warming addresses this. My proposed market trades contracts tied to temperature in a double-sided auction of emissions permits and sequestration contracts. Unlike existing ETSs, the mechanism has a consistent timescale and metric tied to warming, with explicit limits on global temperature in every period into the far future. Every auction finds prices for emissions into the far future. Second, if a jurisdiction does not require firms to manage their emissions, the firms have little incentive to do so. Part 2: A Climate Insidium addresses this. My design incentivizes firms to participate even if their jurisdictions do not join. With sanctions from member jurisdictions and participating firms, the design has bottom-up incentives for joining, and the incentives rise over time under realistic conditions, potentially resulting in a rush to join. Third, existing designs have high transaction costs for implementation, requiring international treaties to begin. Part 3: A Faster Path Forward addresses this. I propose a path without national or international action to begin. A coalition can implement these rules, creating political force to accelerate participation. Full implementation still requires national agreements. This design appears to be closer to "first best", with a lower cost of climate mitigation, than any in the literature, while increasing the certainty of avoiding catastrophic global warming. It might also provide a faster pathway to implementation.

SREC markets are a market-based system designed to incentivize solar energy generation. A regulatory body imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a certificate for each MWh generated. Regulated firms seek to navigate the market to minimize the cost imposed on them, by modulating their SREC generation and trading activities. As such, the SREC market can be viewed through the lens of a large stochastic game with heterogeneous agents, where agents interact through the market price of the certificates. We study this stochastic game by solving the mean-field game (MFG) limit with sub-populations of heterogeneous agents. Our market participants optimize costs accounting for trading frictions, cost of generation, SREC penalty, and generation uncertainty. Using techniques from variational analysis, we characterize firms' optimal controls as the solution of a new class of McKean-Vlasov FBSDE and determine the equilibrium SREC price. We numerically solve the MV-FBSDEs and conclude by demonstrating how firms behave in equilibrium using simulated examples.

This paper is focused on American option pricing in the subdiffusive Black Scholes model. Two methods for valuing American options in the considered model are proposed. The weighted scheme of the finite difference (FD) method is derived and the main properties of the method are presented. The Longstaff-Schwartz method is applied for the discussed model and is compared to the previous method. In the article it is also shown how to valuate wide range of Barrier options using the FD approach. The proposed FD method has $2-\alpha$ order of accuracy with respect to time, where $\alpha\in(0, 1)$ is the subdiffusion parameter, and 2 with respect to space. The paper is a continuation of [13], where the derivation of the governing fractional differential equation, similarly as the stability and convergence analysis can be found.

Managing the prediction of metrics in high-frequency financial markets is a challenging task. An efficient way is by monitoring the dynamics of a limit order book to identify the information edge. This paper describes the first publicly available benchmark dataset of high-frequency limit order markets for mid-price prediction. We extracted normalized data representations of time series data for five stocks from the NASDAQ Nordic stock market for a time period of ten consecutive days, leading to a dataset of ~4,000,000 time series samples in total. A day-based anchored cross-validation experimental protocol is also provided that can be used as a benchmark for comparing the performance of state-of-the-art methodologies. Performance of baseline approaches are also provided to facilitate experimental comparisons. We expect that such a large-scale dataset can serve as a testbed for devising novel solutions of expert systems for high-frequency limit order book data analysis.

In this paper, we propose deep learning algorithms for ranking response surfaces, with applications to optimal stopping problems in financial mathematics. The problem of ranking response surfaces is motivated by estimating optimal feedback policy maps in stochastic control problems, aiming to efficiently find the index associated to the minimal response across the entire continuous input space $\mathcal{X} \subseteq \mathbb{R}^d$. By considering points in $\mathcal{X}$ as pixels and indices of the minimal surfaces as labels, we recast the problem as an image segmentation problem, which assigns a label to every pixel in an image such that pixels with the same label share certain characteristics. This provides an alternative method for efficiently solving the problem instead of using sequential design in our previous work [R. Hu and M. Ludkovski, SIAM/ASA Journal on Uncertainty Quantification, 5 (2017), 212--239].

Deep learning algorithms are scalable, parallel and model-free, i.e., no parametric assumptions needed on the response surfaces. Considering ranking response surfaces as image segmentation allows one to use a broad class of deep neural networks, e.g., UNet, SegNet, DeconvNet, which have been widely applied and numerically proved to possess high accuracy in the field. We also systematically study the dependence of deep learning algorithms on the input data generated on uniform grids or by sequential design sampling, and observe that the performance of deep learning is {\it not} sensitive to the noise and locations (close to/away from boundaries) of training data. We present a few examples including synthetic ones and the Bermudan option pricing problem to show the efficiency and accuracy of this method.

Cryptocurrencies, such as Bitcoin, are becoming increasingly popular, having been widely used as an exchange medium in areas such as financial transaction and asset transfer verification. However, there has been a lack of solutions that can support real-time price prediction to cope with high currency volatility, handle massive heterogeneous data volumes, including social media sentiments, while supporting fault tolerance and persistence in real time, and provide real-time adaptation of learning algorithms to cope with new price and sentiment data. In this paper we introduce KryptoOracle, a novel real-time and adaptive cryptocurrency price prediction platform based on Twitter sentiments. The integrative and modular platform is based on (i) a Spark-based architecture which handles the large volume of incoming data in a persistent and fault tolerant way; (ii) an approach that supports sentiment analysis which can respond to large amounts of natural language processing queries in real time; and (iii) a predictive method grounded on online learning in which a model adapts its weights to cope with new prices and sentiments. Besides providing an architectural design, the paper also describes the KryptoOracle platform implementation and experimental evaluation. Overall, the proposed platform can help accelerate decision-making, uncover new opportunities and provide more timely insights based on the available and ever-larger financial data volume and variety.

We give explicit algorithms and source code for extracting factors underlying Treasury yields using (unsupervised) machine learning (ML) techniques, such as nonnegative matrix factorization (NMF) and (statistically deterministic) clustering. NMF is a popular ML algorithm (used in computer vision, bioinformatics/computational biology, document classification, etc.), but is often misconstrued and misused. We discuss how to properly apply NMF to Treasury yields. We analyze the factors based on NMF and clustering and their interpretation. We discuss their implications for forecasting Treasury yields in the context of out-of-sample ML stability issues.

The expansion of global production networks has raised many important questions about the interdependence among countries and how future changes in the world economy are likely to affect the countries' positioning in global value chains. We are approaching the structure and lengths of value chains from a completely different perspective than has been available so far. By assigning a random endogenous variable to a network linkage representing the number of intermediate sales/purchases before absorption (final use or value added), the discrete-time absorbing Markov chains proposed here shed new light on the world input/output networks. The variance of this variable can help assess the risk when shaping the chain length and optimize the level of production. Contrary to what might be expected simply on the basis of comparative advantage, the results reveal that both the input and output chains exhibit the same quasi-stationary product distribution. Put differently, the expected proportion of time spent in a state before absorption is invariant to changes of the network type. Finally, the several global metrics proposed here, including the probability distribution of global value added/final output, provide guidance for policy makers when estimating the resilience of world trading system and forecasting the macroeconomic developments.

This paper uses stop-level passenger count data in four cities to understand the nation-wide bus ridership decline between 2012 and 2018. The local characteristics associated with ridership change are evaluated in Portland, Miami, Minneapolis/St-Paul, and Atlanta. Poisson models explain ridership as a cross-section and the change thereof as a panel. While controlling for the change in frequency, jobs, and population, the correlation with local socio-demographic characteristics are investigated using data from the American Community Survey. The effect of changing neighborhood demographics on bus ridership are modeled using Longitudinal Employer-Household Dynamics data. At a point in time, neighborhoods with high proportions of non-white, carless, and most significantly, high-school-educated residents are the most likely to have high ridership. Over time, white neighborhoods are losing the most ridership across all four cities. In Miami and Atlanta, places with high concentrations of residents with college education and without access to a car also lose ridership at a faster rate. In Minneapolis/St-Paul, the proportion of college-educated residents is linked to ridership gain. The sign and significance of these results remain consistent even when controlling for intra-urban migration. Although bus ridership is declining across neighborhood characteristics, these results suggest that the underlying cause of bus ridership decline must be primarily affecting the travel behavior of white bus riders.