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Distributional reinforcement learning demonstrates state-of-the-art performance in continuous and discrete control settings with the features of variance and risk, which can be used to explore. However, the exploration method employing the…
A central problem in quantum resource theory is to give operational meaning to quantum resources that can provide clear advantages in certain physical tasks compared to the convex set of resource-free states. We propose to extend this basic…
Coefficient estimation and variable selection in multiple linear regression is routinely done in the (penalized) least squares (LS) framework. The concept of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96…
We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…
We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method - named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization) - for analyzing high- dimensional data. Unlike in the linear setting where…
This paper examines optimal risk sharing for empirically realistic risk attitudes, providing results on Pareto optimality, competitive equilibria, utility frontiers, and the first and second theorems of welfare. Contrary to common…
Financial market prediction and optimal trading strategy development remain challenging due to market complexity and volatility. Our research in quantum finance and reinforcement learning for decision-making demonstrates the approach of…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
Unit commitment (UC) optimizes the start-up and shutdown schedules of generating units to meet load demand while minimizing costs. However, the increasing integration of renewable energy introduces uncertainties for real-time scheduling.…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response $Y$ given covariates $X$, without making distributional assumptions. However, existing constructions of CQR can be…
Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…
This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…
Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…
We consider the problem of optimally sharing a financial position among agents with potentially different reference risk measures. The problem is equivalent to computing the infimal convolution of the risk metrics and finding the so-called…
We study Pareto-optimal risk sharing in economies with heterogeneous attitudes toward risk, where agents' preferences are modeled by distortion risk measures. Building on comonotonic and counter-monotonic improvement results, we show that…
Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…
In our previous paper, "A Unified Approach to Systemic Risk Measures via Acceptance Set" (\textit{Mathematical Finance, 2018}), we have introduced a general class of systemic risk measures that allow for random allocations to individual…
The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in…