Monte Carlo Approximate Tensor Moment Simulations

An algorithm to generate samples with approximate first-, second-, and third-order moments is presented extending the Cholesky matrix decomposition to a Cholesky tensor decomposition of an arbitrary order. The tensor decomposition of the first-, second-, and third-order objective moments generates a non-linear system of equations. The algorithm solves these equations by numerical methods. The results show that the optimisation algorithm delivers samples with an approximate error of 0.1%/4% between the components of the objective and the sample moments. An application for sensitivity analysis of portfolio risk assessment with Value-at-Risk (VaR) is provided. A comparison with previous methods available in the literature suggests that methodology proposed reduces the error of the objective moments in the generated samples.