The stochastic implicit Euler method - A stable coupling scheme for Monte Carlo burnup calculations

Existing Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the coupling schemes of the existing Monte Carlo burnup codes can be numerically unstable. Here we develop the Stochastic Implicit Euler method - a stable and efficient new coupling scheme. The implicit solution is obtained by the stochastic approximation at each time step. Our test calculations demonstrate that the Stochastic Implicit Euler method can provide an accurate solution to problems where the methods in the existing Monte Carlo burnup codes fail. © 2013 Elsevier Ltd. All rights reserved.

Gaussian process volatility model

The prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the evolution of the variance. Moreover, functional parameters are usually learned by maximum likelihood, which can lead to over-fitting. To address these problems we introduce GP-Vol, a novel non-parametric model for time-changing variances based on Gaussian Processes. This new model can capture highly flexible functional relationships for the variances. Furthermore, we introduce a new online algorithm for fast inference in GP-Vol. This method is much faster than current offline inference procedures and it avoids overfitting problems by following a fully Bayesian approach. Experiments with financial data show that GP-Vol performs significantly better than current standard alternatives.