Wrong way risk can be incorporated in Credit Value Adjustment (CVA) calculations in a reduced form model. Hull and White [16] introduced a CVA model that captures wrong way risk by expressing the stochastic intensity of a counterparty’s default time in terms of the financial institution’s credit exposure to the counterparty. We consider a class of reduced form CVA models that includes the formu...

We present a numerical algorithm for nonnegative matrix factorization (NMF) problems under noisy separability. An NMF problem under separability can be stated as one of finding all vertices of the convex hull of data points. The research interest of this paper is to find the vectors as close to the vertices as possible in a situation in which noise is added to the data points. Our algorithm is ...

We consider the problem of computing a restricted nonnegative matrix factorization (NMF) of an m × n matrix X . Specifically, we seek a factorization X ≈ BC, where the k columns of B are a subset of those from X and C ∈ Rk×n ≥0 . Equivalently, given the matrix X , consider the problem of finding a small subset, S, of the columns of X such that the conic hull of S ε-approximates the conic hull o...

We prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contr...

Ship motion problem is approached exploiting the assumption of linearity and subdividing forces acting on the hull in different components; in this paper the focus is on the radiation problem. A fully viscous solver, based on the numerical solution of the Navier-Stokes equation through the finite volume technique, is used to calculate radiation forces on hull surface, with non linear free surfa...

Using elementary duality properties of positive semidefinite moment matrices and polynomial sum-of-squares decompositions, we prove that the convex hull of rationally parameterized algebraic varieties is semidefinite representable (that is, it can be represented as a projection of an affine section of the cone of positive semidefinite matrices) in the case of (a) curves; (b) hypersurfaces param...

In this paper we present various algorithms for multiplying multivariate polynomials and series. All algorithms have been implemented in the C++ libraries of the Mathemagix system. We describe naive and softly optimal variants for various types of coefficients and supports and compare their relative performances. For the first time we are able to observe the benefit of non naive arithmetic for ...

Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developped can be implemented and parallelize...

This study proposes a method for the acceleration of the projection method to compute a few eigenvalues with the largest real parts of a large nonsymmetric matrix. In the eld of the solution of the linear system, an acceleration using the least squares polynomial which minimizes its norm on the boundary of the convex hull formed with the unwanted eigenvalues are proposed. We simplify this metho...

This paper studies the polynomial basis that generates smallest n-simplex enclosing a given nth-degree curve in Rn. Although Bernstein and B-Spline bases provide feasible solutions to this problem, simplexes obtained by these are not possible, which leads overly conservative results many CAD (computer-aided design) applications. We first prove solves problem (MINVO basis) also for with largest ...