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A new modelling approach that directly prescribes dynamics to the term structure of VIX futures is proposed in this paper. The approach is motivated by the tractability enjoyed by models that directly prescribe dynamics to the VIX,…
Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances and point correspondences via the geodesic boundary value problem, solving…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
We investigate the data-driven discovery of parametric representations for implied volatility slices. Using symbolic regression, we search for simple analytic formulas that approximate the total implied variance as a function of…
Score calibration enables automatic speaker recognizers to make cost-effective accept / reject decisions. Traditional calibration requires supervised data, which is an expensive resource. We propose a 2-component GMM for unsupervised…
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
In this paper, we focus on finding the global minimizer of a general unconstrained nonsmooth nonconvex optimization problem. Taking advantage of the smoothing method and the consensus-based optimization (CBO) method, we propose a novel…
ESG ratings provide a quantitative measure for socially responsible investment. We present a unified framework for incorporating numeric ESG ratings into dynamic pricing theory. Specifically, we introduce an ESG-valued return that is a…
We construct infinite periodic versions of the stress matrix and establish sufficient conditions for periodic tensegrity frameworks to be globally rigid in $\mathbb{R}^d$ in the cases when the lattice is either fixed, fully flexible, or…
We introduced an $\tilde{\mathcal{A}}$-invariant for quasi-ordinary parameterizations and we consider it to describe quasi-ordinary surfaces with one generalized characteristic exponent admitting a countable moduli.
We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…
In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our…
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.
In this paper, we present a study of an a posteriori estimator for the discretization error of a non-standard finite difference scheme applied to boundary value problems defined on an infinite interval. In particular, we show how…
We study analytically the equilibrium and near-equilibrium properties of a model of surfaces relaxing via linear surface diffusion and subject to a lattice potential. We employ the variational mean field formalism introduced by Saito for…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential L\'evy processes are calibrated using regularized weighted…
Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas, options on realized variance or VIX options. These…