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In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature.…
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications. Previous primal-dual style approaches suffer from instability issues and lack optimality…
Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular [Rahimi and Recht, 2007], where kernel approximation is treated as empirical…
In many practical applications of numerical methods a substantial increase in efficiency can be obtained by using local grid refinement, since the solution is generally smooth in large parts of the domain and large gradients occur only…
Consider a multi-agent network comprised of risk averse social sensors and a controller that jointly seek to estimate an unknown state of nature, given noisy measurements. The network of social sensors perform Bayesian social learning -…
We study the allocation of synthetic portfolios under hierarchical nested, one-factor, and diagonal structures of the population covariance matrix in a high-dimensional scenario. The noise reduction approaches for the sample realizations…
We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition…
This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor…
Accurate covariance forecasting is central to portfolio allocation, risk management, and asset pricing, yet many existing methods struggle at medium-term horizons, where shifting market regimes and slower dynamics predominate. We propose a…
This paper presents a scheme to design a tracking controller for a class of uncertain nonlinear systems using a robust feedback linearization approach. The scheme is composed of two steps. In the first step, a linearized uncertainty model…
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte…
Conformal risk control is an extension of conformal prediction for controlling risk functions beyond miscoverage. The original algorithm controls the expected value of a loss that is monotonic in a one-dimensional parameter. Here, we…
Monte Carlo Approaches for calculating Value-at-Risk (VaR) are powerful tools widely used by financial risk managers across the globe. However, they are time consuming and sometimes inaccurate. In this paper, a fast and accurate Monte Carlo…
We consider an optimal investment and risk control problem for an insurer under the mean-variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem…
The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
We consider monotone mean-variance (MMV) portfolio selection problems with a conic convex constraint under diffusion models, and their counterpart problems under mean-variance (MV) preferences. We obtain the precommitted optimal strategies…
Two-dimensional singular decomposition (2DSVD) has been widely used for image processing tasks, such as image reconstruction, classification, and clustering. However, traditional 2DSVD algorithm is based on the mean square error (MSE) loss,…
Tuning parameter selection is of critical importance for kernel ridge regression. To this date, data driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the…