Sodium-ion batteries (SIBs) are suitable candidates for the field of large-scale energy storage due to infinite global reserves and low-cost of sodium. Prussian blue (PB) and its analogues are promising cathode materials for SIBs because of their environmental friendliness, open framework, and...

We consider the problem of optimally selecting a large portfolio of risky loans, such as mortgages, credit cards, auto loans, student loans, or business loans. Examples include loan portfolios held by financial institutions and fixed-income investors as well as pools of loans backing mortgage-...

We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear stochastic PDE, and certain moments of the limiting...

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of...

This paper develops a new neural network architecture for modeling spatial distributions (i.e., distributions on R^d) which is computationally efficient. The design of the architecture takes advantage of the specific structure of limit order books. The new architecture, which we refer to as a...

Financial institutions, government-sponsored enterprises, and asset-backed security in- vestors are often exposed to delinquency and prepayment risk from large numbers of loans. Examples include mortgages, credit cards, auto, student, and business loans. Due to the size of the pools, the...

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream...