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We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…
The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic…
Treating class with a single center may hardly capture data distribution complexities. Using multiple sub-centers is an alternative way to address this problem. However, highly correlated sub-classes, the classifier's parameters grow…
It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)] that within the framework of the semigroup Markovian master equation, decoherence-free (DF) subspaces exist which are stable to first order in time to a…
We propose a new class of robust and Fisher-consistent estimators for mixture models. These estimators can be used to construct robust model-based clustering procedures. We study in detail the case of multivariate normal mixtures and…
A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process…
We investigate the stability of Quantum Critical Points (QCPs) in the presence of two competing phases. These phases near QCPs are assumed to be either classical or quantum and assumed to repulsively interact via square-square interactions.…
We establish a condition for the perturbative stability of zero energy nodal points in the quasi-particle spectrum of superconductors in the presence of coexisting \textit{commensurate} orders. The nodes are found to be stable if the…
This paper is devoted to studying three-dimensional non-commensurate fractional order differential equation systems with Caputo derivatives. Necessary and sufficient conditions are for the asymptotic stability of such systems are obtained.
Efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff-Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. We solve the model…
The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization…
To analyze the uncertain data frequently encountered in practice, this paper proposes novel fixed-effects models that incorporate an uncertain measure to investigate variables of interest and nuisance variables in factor designs. First, an…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
A new understanding of the notion of the stable solution to ill-posed problems is proposed. The new notion is more realistic than the old one and better fits the practical computational needs. A method for constructing stable solutions in…
We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on…