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Chance constraints are widely used in stochastic model predictive control (MPC) to enforce probabilistic state and input constraints in the presence of unbounded disturbances. However, they only restrict violation probabilities and do not…

It is well known that modeling and forecasting realized covariance matrices of asset returns play a crucial role in the field of finance. The availability of high frequency intraday data enables the modeling of the realized covariance…

Deep learning potentials for complex many-body systems often face challenges of insufficient accuracy and a lack of physical realism. This paper proposes an "Observable-Constrained Variational Framework" (OCVF), a general top-down…

Predicting future frames for a video sequence is a challenging generative modeling task. Promising approaches include probabilistic latent variable models such as the Variational Auto-Encoder. While VAEs can handle uncertainty and model…

We propose a new class of financial volatility models, called the REcurrent Conditional Heteroskedastic (RECH) models, to improve both in-sample analysis and out-ofsample forecasting of the traditional conditional heteroskedastic models. In…

To the naked eye, stock prices are considered chaotic, dynamic, and unpredictable. Indeed, it is one of the most difficult forecasting tasks that hundreds of millions of retail traders and professional traders around the world try to do…

Volatility asymmetry is a hot topic in high-frequency financial market. In this paper, we propose a new econometric model, which could describe volatility asymmetry based on high-frequency historical data and low-frequency historical data.…

We present a stochastic volatility market model where volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. With this model we exactly measure the leverage effect and other stylized facts, such as mean…

This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite…

The Inverse Optimal Control (IOC) problem is a structured system identification problem that aims to identify the underlying objective function based on observed optimal trajectories. This provides a data-driven way to model experts'…

Financial markets are difficult to predict due to its complex systems dynamics. Although there have been some recent studies that use machine learning techniques for financial markets prediction, they do not offer satisfactory performance…

We propose an enhancement to wholesale electricity markets whereby the exposure of consumers to increasingly large and volatile consumer payments arising as a byproduct of volatile real-time net loads -- i.e., loads minus renewable outputs…

We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective…

Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…

Modeling heterogeneous correlated time series requires the ability to learn hidden dynamic relationships between component time series with possibly varying periodicities and generative processes. To address this challenge, we formulate and…

We address the challenges of modeling high-frequency integer price changes in financial markets using continuous distributions, particularly the Student's t-distribution. We demonstrate that traditional GARCH models, which rely on…

The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is…

Variational inference often minimizes the "reverse" Kullbeck-Leibler (KL) KL(q||p) from the approximate distribution q to the posterior p. Recent work studies the "forward" KL KL(p||q), which unlike reverse KL does not lead to variational…

Nowadays, with the availability of massive amount of trade data collected, the dynamics of the financial markets pose both a challenge and an opportunity for high frequency traders. In order to take advantage of the rapid, subtle movement…

Control invariant set is critical for guaranteeing safe control and the problem of computing control invariant set for linear discrete-time system is revisited in this paper by using a data-driven approach. Specifically, sample points on…