Patent Document ID: 8788391
Application ID: 12946878
Patent Status: 1

Claim One:
1. numerical modelling apparatus, the apparatus comprising: an input unit arranged to receive signals containing data having information relating to a set of assets; processor unit coupled to the input unit and arranged to: a) provide matrix V having plurality of elements, wherein each of the elements represents relationship of risk related to respective pair of the assets, and wherein each element is given by scalar product of two risk vectors, such that each of the assets has an associated risk vector according to the elements of the matrix; b) decompose the matrix V into eigenvectors and eigenvalues according to: 
 V=E·Λ·E′ wherein E is set of eigenvectors of the matrix V in columns, Λ is the corresponding diagonal eigenvalue matrix, and E′ is the transpose of E; c) provide dataset of portfolio weights w for each of the assets according to: 
 w∝E·Λ −1/2 ·1 where E is set of eigenvectors of the matrix V in columns and Λ is the diagonal eigenvalue matrix and 1 is column vector all of whose elements are equal to one, wherein the portfolio weightings w are provided as column vector from: D = w ′ · E · Λ 1 / 2 · 1 w ′ · V · w where w represents column vector containing portfolio weights, E is the eigenvector matrix and Λ is corresponding diagonal eigenvalue matrix of the matrix V for the set of assets, and D is an Objective Function relating to the set of assets; and d) derive components of each of the risk vectors in the basis of unit independent risks by the corresponding row of the matrix product E·Λ 1/2 relating to each of the assets; and an output unit coupled to the processor unit and arranged to output the components of each of the risk vectors as risk vector dataset onto tangible computer-readable recording medium or display device.