An adaptive algorithm to accelerate multi-parameter Monte Carlo computations

Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations

This paper shows that it is relatively easy to incorporate adaptive timesteps into multilevel Monte Carlo simulations without violating the telescoping sum on which multilevel Monte Carlo is based. The numerical approach is presented for both SDEs and continuous-time Markov processes. Numerical experiments are given for each, with the full code available for those who are interested in seeing t...

An adaptive Monte Carlo algorithm for computing mixed logit estimators

Researchers and analysts are increasingly using mixed logit models for estimating responses to forecast demand and to determine the factors that affect individual choices. However the numerical cost associated to their evaluation can be prohibitive, the inherent probability choices being represented by multidimensional integrals. This cost remains high even if Monte Carlo or quasi-Monte Carlo t...

An adaptive Monte Carlo integration algorithm with general division approach

We propose an adaptive Monte Carlo algorithm for estimating multidimensional integrals over a hyper-rectangular region. The lgorithm uses iteratively the idea of separating the domain of integration into 2subregions. The proposed algorithm can be applied irectly to estimate the integral using an efficient way of storage. We test the algorithm for estimating the value of a 30-dimensional ntegral...

Implementation and analysis of an adaptive multilevel Monte Carlo algorithm

We present an adaptive multilevel Monte Carlo (MLMC) method for weak approximations of solutions to Itô stochastic differential equations (SDE). The work [Oper. Res. 56 (2008), 607–617] proposed and analyzed an MLMC method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a single level Euler–Maruyama Monte Carlo method from...

On Monte Carlo and Quasi-Monte Carlo for Matrix Computations