Related papers: Chebyshev Methods for Ultra-efficient Risk Calcula…
It is needed to solve generalized eigenvalue problems (GEP) in many applications, such as the numerical simulation of vibration analysis, quantum mechanics, electronic structure, etc. The subspace iteration is a kind of widely used…
The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive in the high-frequency regime, Levin methods provide a way to…
Portfolio management is an important yet challenging task in AI for FinTech, which aims to allocate investors' budgets among different assets to balance the risk and return of an investment. In this study, we propose a general…
Every "x"-adjustment in the so-called xVA financial risk management framework relies on the computation of exposures. Considering thousands of Monte Carlo paths and tens of simulation steps, a financial portfolio needs to be evaluated…
We consider multicriteria problems of evaluating absolute ratings (scores, priorities, weights) of given alternatives for making decisions, which are compared in pairs under several criteria. Given matrices of pairwise comparisons of…
This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an…
Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates outer scenarios and the inner-level simulations are run in each outer…
In this paper, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method…
The present paper concerns filtered de la Vall\'ee Poussin (VP) interpolation at the Chebyshev nodes of the four kinds. This approximation model is interesting for applications because it combines the advantages of the classical Lagrange…
Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…
The recent explosion in the amount and dimensionality of data has exacerbated the need of trading off computational and statistical efficiency carefully, so that inference is both tractable and meaningful. We propose a framework that…
Risk measures are important key figures to measure the adequacy of the reserves of a company. The most common risk measures in practice are Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Recently, quantum-based algorithms are…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…
Cross-validation (CV) is one of the main tools for performance estimation and parameter tuning in machine learning. The general recipe for computing CV estimate is to run a learning algorithm separately for each CV fold, a computationally…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
We study Lissajous curves in the 3-cube, that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…